10x^2-10x-71=0

Solution for 10x^2-10x-71=0 equation:

10x^2-10x-71=0

a = 10; b = -10; c = -71;
Δ = b2-4ac
Δ = -102-4·10·(-71)
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14\sqrt{15}}{2*10}=\frac{10-14\sqrt{15}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14\sqrt{15}}{2*10}=\frac{10+14\sqrt{15}}{20}
$