10x^2-10x-5=0

Solution for 10x^2-10x-5=0 equation:

10x^2-10x-5=0

a = 10; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·10·(-5)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{3}}{2*10}=\frac{10-10\sqrt{3}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{3}}{2*10}=\frac{10+10\sqrt{3}}{20}
$