(x-3)(2x+5)=15

Solution for (x-3)(2x+5)=15 equation:

(x-3)(2x+5)=15

We move all terms to the left:

(x-3)(2x+5)-(15)=0

We multiply parentheses ..

(+2x^2+5x-6x-15)-15=0

We get rid of parentheses

2x^2+5x-6x-15-15=0

We add all the numbers together, and all the variables

2x^2-1x-30=0

a = 2; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·2·(-30)
Δ = 241
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{241}}{2*2}=\frac{1-\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{241}}{2*2}=\frac{1+\sqrt{241}}{4}
$