(2x-3)(x+1)=187

Solution for (2x-3)(x+1)=187 equation:

(2x-3)(x+1)=187

We move all terms to the left:

(2x-3)(x+1)-(187)=0

We multiply parentheses ..

(+2x^2+2x-3x-3)-187=0

We get rid of parentheses

2x^2+2x-3x-3-187=0

We add all the numbers together, and all the variables

2x^2-1x-190=0

a = 2; b = -1; c = -190;
Δ = b2-4ac
Δ = -12-4·2·(-190)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-39}{2*2}=\frac{-38}{4}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+39}{2*2}=\frac{40}{4}
=10
$