x^2+30x-171=0

Solution for x^2+30x-171=0 equation:

x^2+30x-171=0

a = 1; b = 30; c = -171;
Δ = b2-4ac
Δ = 302-4·1·(-171)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{11}}{2*1}=\frac{-30-12\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{11}}{2*1}=\frac{-30+12\sqrt{11}}{2}
$