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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

(+2X^2-3X+4X-6)-204=0

We get rid of parentheses

2X^2-3X+4X-6-204=0

We add all the numbers together, and all the variables

2X^2+X-210=0

a = 2; b = 1; c = -210;
Δ = b2-4ac
Δ = 12-4·2·(-210)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*2}=\frac{-42}{4}
=-10+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*2}=\frac{40}{4}
=10
$