5x^2-62x+23=0

Solution for 5x^2-62x+23=0 equation:

5x^2-62x+23=0

a = 5; b = -62; c = +23;
Δ = b2-4ac
Δ = -622-4·5·23
Δ = 3384
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:

$\sqrt{\Delta}=\sqrt{3384}=\sqrt{36*94}=\sqrt{36}*\sqrt{94}=6\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-6\sqrt{94}}{2*5}=\frac{62-6\sqrt{94}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+6\sqrt{94}}{2*5}=\frac{62+6\sqrt{94}}{10}
$