(x-5)(2x+3)=84

Solution for (x-5)(2x+3)=84 equation:

(x-5)(2x+3)=84

We move all terms to the left:

(x-5)(2x+3)-(84)=0

We multiply parentheses ..

(+2x^2+3x-10x-15)-84=0

We get rid of parentheses

2x^2+3x-10x-15-84=0

We add all the numbers together, and all the variables

2x^2-7x-99=0

a = 2; b = -7; c = -99;
Δ = b2-4ac
Δ = -72-4·2·(-99)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-29}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+29}{2*2}=\frac{36}{4}
=9
$