x^2+18x-27=10

Solution for x^2+18x-27=10 equation:

x^2+18x-27=10

We move all terms to the left:

x^2+18x-27-(10)=0

We add all the numbers together, and all the variables

x^2+18x-37=0

a = 1; b = 18; c = -37;
Δ = b2-4ac
Δ = 182-4·1·(-37)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{118}}{2*1}=\frac{-18-2\sqrt{118}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{118}}{2*1}=\frac{-18+2\sqrt{118}}{2}
$