5x^2-4+2x^2=9x^2-56

Solution for 5x^2-4+2x^2=9x^2-56 equation:

5x^2-4+2x^2=9x^2-56

We move all terms to the left:

5x^2-4+2x^2-(9x^2-56)=0

We add all the numbers together, and all the variables

7x^2-(9x^2-56)-4=0

We get rid of parentheses

7x^2-9x^2+56-4=0

We add all the numbers together, and all the variables

-2x^2+52=0

a = -2; b = 0; c = +52;
Δ = b2-4ac
Δ = 02-4·(-2)·52
Δ = 416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*-2}=\frac{0-4\sqrt{26}}{-4}
=-\frac{4\sqrt{26}}{-4}
=-\frac{\sqrt{26}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*-2}=\frac{0+4\sqrt{26}}{-4}
=\frac{4\sqrt{26}}{-4}
=\frac{\sqrt{26}}{-1}
$