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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x+3)(x-2)-7056=0

We multiply parentheses ..

(+x^2-2x+3x-6)-7056=0

We get rid of parentheses

x^2-2x+3x-6-7056=0

We add all the numbers together, and all the variables

x^2+x-7062=0

a = 1; b = 1; c = -7062;
Δ = b2-4ac
Δ = 12-4·1·(-7062)
Δ = 28249
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{-(1)-\sqrt{28249}}{2*1}=\frac{-1-\sqrt{28249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{28249}}{2*1}=\frac{-1+\sqrt{28249}}{2}
$