-7x2-38x-13=0

Solution for -7x2-38x-13=0 equation:

-7x^2-38x-13=0

a = -7; b = -38; c = -13;
Δ = b2-4ac
Δ = -382-4·(-7)·(-13)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-6\sqrt{30}}{2*-7}=\frac{38-6\sqrt{30}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+6\sqrt{30}}{2*-7}=\frac{38+6\sqrt{30}}{-14}
$