x(x+5)+x^2=133

Solution for x(x+5)+x^2=133 equation:

x(x+5)+x^2=133

We move all terms to the left:

x(x+5)+x^2-(133)=0

We multiply parentheses

x^2+x^2+5x-133=0

We add all the numbers together, and all the variables

2x^2+5x-133=0

a = 2; b = 5; c = -133;
Δ = b2-4ac
Δ = 52-4·2·(-133)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-33}{2*2}=\frac{-38}{4}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+33}{2*2}=\frac{28}{4}
=7
$