10a^2-10a-23=0

Solution for 10a^2-10a-23=0 equation:

10a^2-10a-23=0

a = 10; b = -10; c = -23;
Δ = b2-4ac
Δ = -102-4·10·(-23)
Δ = 1020
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{255}}{2*10}=\frac{10-2\sqrt{255}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{255}}{2*10}=\frac{10+2\sqrt{255}}{20}
$