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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-10x-3x+15)-15=0

We get rid of parentheses

2x^2-10x-3x+15-15=0

We add all the numbers together, and all the variables

2x^2-13x=0

a = 2; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*2}=\frac{26}{4}
=6+1/2
$