5x^2-23x-3=8

Solution for 5x^2-23x-3=8 equation:

5x^2-23x-3=8

We move all terms to the left:

5x^2-23x-3-(8)=0

We add all the numbers together, and all the variables

5x^2-23x-11=0

a = 5; b = -23; c = -11;
Δ = b2-4ac
Δ = -232-4·5·(-11)
Δ = 749
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{749}}{2*5}=\frac{23-\sqrt{749}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{749}}{2*5}=\frac{23+\sqrt{749}}{10}
$