(x+10)(x+5)=84

Solution for (x+10)(x+5)=84 equation:

(x+10)(x+5)=84

We move all terms to the left:

(x+10)(x+5)-(84)=0

We multiply parentheses ..

(+x^2+5x+10x+50)-84=0

We get rid of parentheses

x^2+5x+10x+50-84=0

We add all the numbers together, and all the variables

x^2+15x-34=0

a = 1; b = 15; c = -34;
Δ = b2-4ac
Δ = 152-4·1·(-34)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-19}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+19}{2*1}=\frac{4}{2}
=2
$