x(2x+7)=15^2

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

x(2x+7)=15^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(2x+7)-225=0

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