X^2+18x-91=0

Solution for X^2+18x-91=0 equation:

X^2+18X-91=0

a = 1; b = 18; c = -91;
Δ = b2-4ac
Δ = 182-4·1·(-91)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{43}}{2*1}=\frac{-18-4\sqrt{43}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{43}}{2*1}=\frac{-18+4\sqrt{43}}{2}
$