x(x+2)+(x-8)=50

Solution for x(x+2)+(x-8)=50 equation:

x(x+2)+(x-8)=50

We move all terms to the left:

x(x+2)+(x-8)-(50)=0

We multiply parentheses

x^2+2x+(x-8)-50=0

We get rid of parentheses

x^2+2x+x-8-50=0

We add all the numbers together, and all the variables

x^2+3x-58=0

a = 1; b = 3; c = -58;
Δ = b2-4ac
Δ = 32-4·1·(-58)
Δ = 241
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{-(3)-\sqrt{241}}{2*1}=\frac{-3-\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{241}}{2*1}=\frac{-3+\sqrt{241}}{2}
$