Underroot 2x^2 + 2x + 5x + 5 U.R2
=under root 2 x (x+ under root 2 ) + under root 5 ( x + under root 2)
=( U.R 2x + U.R5) (x+U.R2)
x =U.R5/U.R2 or - U.R2. (U.r = under root)

Quadratic Equation:
A quadratic equation is a polynomial equation of the second degree. It can be written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Given Equation:
The given equation is √2x² + 7x + 5√2 = 0.

Using Quadratic Formula:
To solve the given equation using the quadratic formula, we can follow these steps:

Step 1: Identify the coefficients and constants:
The coefficients in the given equation are:
a = √2
b = 7
c = 5√2

Step 2: Substitute the values in the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we get:
x = (-(7) ± √((7)² - 4(√2)(5√2))) / (2(√2))

Simplifying further:
x = (-7 ± √(49 - 4(2)(5))) / (2√2)
x = (-7 ± √(49 - 40)) / (2√2)
x = (-7 ± √9) / (2√2)
x = (-7 ± 3) / (2√2)

Step 3: Simplify the expression:
We can simplify the expression by rationalizing the denominator:
x = (-7 ± 3) / (2√2) * (√2/√2)
x = (-7 ± 3√2) / (2 * 2)
x = (-7 ± 3√2) / 4

Step 4: Final Solution:
The final solutions are:
x₁ = (-7 + 3√2) / 4
x₂ = (-7 - 3√2) / 4

Conclusion:
The equation √2x² + 7x + 5√2 = 0 can be solved using the quadratic formula. The solutions are x₁ = (-7 + 3√2) / 4 and x₂ = (-7 - 3√2) / 4.