x^2+x^2+18x+54=180

Solution for x^2+x^2+18x+54=180 equation:

x^2+x^2+18x+54=180

We move all terms to the left:

x^2+x^2+18x+54-(180)=0

We add all the numbers together, and all the variables

2x^2+18x-126=0

a = 2; b = 18; c = -126;
Δ = b2-4ac
Δ = 182-4·2·(-126)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{37}}{2*2}=\frac{-18-6\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{37}}{2*2}=\frac{-18+6\sqrt{37}}{4}
$