(2x-1)(x+2)=15

Solution for (2x-1)(x+2)=15 equation:

(2x-1)(x+2)=15

We move all terms to the left:

(2x-1)(x+2)-(15)=0

We multiply parentheses ..

(+2x^2+4x-1x-2)-15=0

We get rid of parentheses

2x^2+4x-1x-2-15=0

We add all the numbers together, and all the variables

2x^2+3x-17=0

a = 2; b = 3; c = -17;
Δ = b2-4ac
Δ = 32-4·2·(-17)
Δ = 145
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{-(3)-\sqrt{145}}{2*2}=\frac{-3-\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{145}}{2*2}=\frac{-3+\sqrt{145}}{4}
$