(x+59)(+x+51)+84=180

Solution for (x+59)(+x+51)+84=180 equation:

(x+59)(+x+51)+84=180

We move all terms to the left:

(x+59)(+x+51)+84-(180)=0

We add all the numbers together, and all the variables

(x+59)(x+51)+84-180=0

We add all the numbers together, and all the variables

(x+59)(x+51)-96=0

We multiply parentheses ..

(+x^2+51x+59x+3009)-96=0

We get rid of parentheses

x^2+51x+59x+3009-96=0

We add all the numbers together, and all the variables

x^2+110x+2913=0

a = 1; b = 110; c = +2913;
Δ = b2-4ac
Δ = 1102-4·1·2913
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-8\sqrt{7}}{2*1}=\frac{-110-8\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+8\sqrt{7}}{2*1}=\frac{-110+8\sqrt{7}}{2}
$