X^2-14x-135=0

Solution for X^2-14x-135=0 equation:

X^2-14X-135=0

a = 1; b = -14; c = -135;
Δ = b2-4ac
Δ = -142-4·1·(-135)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{46}}{2*1}=\frac{14-4\sqrt{46}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{46}}{2*1}=\frac{14+4\sqrt{46}}{2}
$