x*(x+1)+x*(x+1)=30

Solution for x*(x+1)+x*(x+1)=30 equation:

x(x+1)+x(x+1)=30

We move all terms to the left:

x(x+1)+x(x+1)-(30)=0

We multiply parentheses

x^2+x^2+x+x-30=0

We add all the numbers together, and all the variables

2x^2+2x-30=0

a = 2; b = 2; c = -30;
Δ = b2-4ac
Δ = 22-4·2·(-30)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*2}=\frac{-2-2\sqrt{61}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*2}=\frac{-2+2\sqrt{61}}{4}
$