(x-7)(2x+3)=2x+100

Solution for (x-7)(2x+3)=2x+100 equation:

(x-7)(2x+3)=2x+100

We move all terms to the left:

(x-7)(2x+3)-(2x+100)=0

We get rid of parentheses

(x-7)(2x+3)-2x-100=0

We multiply parentheses ..

(+2x^2+3x-14x-21)-2x-100=0

We get rid of parentheses

2x^2+3x-14x-2x-21-100=0

We add all the numbers together, and all the variables

2x^2-13x-121=0

a = 2; b = -13; c = -121;
Δ = b2-4ac
Δ = -132-4·2·(-121)
Δ = 1137
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{-(-13)-\sqrt{1137}}{2*2}=\frac{13-\sqrt{1137}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1137}}{2*2}=\frac{13+\sqrt{1137}}{4}
$