(2x-9)(x+5)=15

Solution for (2x-9)(x+5)=15 equation:

(2x-9)(x+5)=15

We move all terms to the left:

(2x-9)(x+5)-(15)=0

We multiply parentheses ..

(+2x^2+10x-9x-45)-15=0

We get rid of parentheses

2x^2+10x-9x-45-15=0

We add all the numbers together, and all the variables

2x^2+x-60=0

a = 2; b = 1; c = -60;
Δ = b2-4ac
Δ = 12-4·2·(-60)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{481}}{2*2}=\frac{-1-\sqrt{481}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{481}}{2*2}=\frac{-1+\sqrt{481}}{4}
$