15^2=2x^2+7x

Solution for 15^2=2x^2+7x equation:

15^2=2x^2+7x

We move all terms to the left:

15^2-(2x^2+7x)=0

We add all the numbers together, and all the variables

-(2x^2+7x)+225=0

We get rid of parentheses

-2x^2-7x+225=0

a = -2; b = -7; c = +225;
Δ = b2-4ac
Δ = -72-4·(-2)·225
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-43}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+43}{2*-2}=\frac{50}{-4}
=-12+1/2
$