10x2-78x-91=0

Solution for 10x2-78x-91=0 equation:

10x^2-78x-91=0

a = 10; b = -78; c = -91;
Δ = b2-4ac
Δ = -782-4·10·(-91)
Δ = 9724
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:

$\sqrt{\Delta}=\sqrt{9724}=\sqrt{4*2431}=\sqrt{4}*\sqrt{2431}=2\sqrt{2431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{2431}}{2*10}=\frac{78-2\sqrt{2431}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{2431}}{2*10}=\frac{78+2\sqrt{2431}}{20}
$