20y^2-92y-23=0

Solution for 20y^2-92y-23=0 equation:

20y^2-92y-23=0

a = 20; b = -92; c = -23;
Δ = b2-4ac
Δ = -922-4·20·(-23)
Δ = 10304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10304}=\sqrt{64*161}=\sqrt{64}*\sqrt{161}=8\sqrt{161}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-8\sqrt{161}}{2*20}=\frac{92-8\sqrt{161}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+8\sqrt{161}}{2*20}=\frac{92+8\sqrt{161}}{40}
$