(X+2)(2x-3)=102

Solution for (X+2)(2x-3)=102 equation:

(X+2)(2X-3)=102

We move all terms to the left:

(X+2)(2X-3)-(102)=0

We multiply parentheses ..

(+2X^2-3X+4X-6)-102=0

We get rid of parentheses

2X^2-3X+4X-6-102=0

We add all the numbers together, and all the variables

2X^2+X-108=0

a = 2; b = 1; c = -108;
Δ = b2-4ac
Δ = 12-4·2·(-108)
Δ = 865
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{865}}{2*2}=\frac{-1-\sqrt{865}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{865}}{2*2}=\frac{-1+\sqrt{865}}{4}
$