(x+7)*(2x-3)=84

Solution for (x+7)*(2x-3)=84 equation:

(x+7)(2x-3)=84

We move all terms to the left:

(x+7)(2x-3)-(84)=0

We multiply parentheses ..

(+2x^2-3x+14x-21)-84=0

We get rid of parentheses

2x^2-3x+14x-21-84=0

We add all the numbers together, and all the variables

2x^2+11x-105=0

a = 2; b = 11; c = -105;
Δ = b2-4ac
Δ = 112-4·2·(-105)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-31}{2*2}=\frac{-42}{4}
=-10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*2}=\frac{20}{4}
=5
$