X^2+33x=27

Solution for X^2+33x=27 equation:

X^2+33X=27

We move all terms to the left:

X^2+33X-(27)=0

a = 1; b = 33; c = -27;
Δ = b2-4ac
Δ = 332-4·1·(-27)
Δ = 1197
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:

$\sqrt{\Delta}=\sqrt{1197}=\sqrt{9*133}=\sqrt{9}*\sqrt{133}=3\sqrt{133}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{133}}{2*1}=\frac{-33-3\sqrt{133}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{133}}{2*1}=\frac{-33+3\sqrt{133}}{2}
$