5x^2=3x+23

Solution for 5x^2=3x+23 equation:

5x^2=3x+23

We move all terms to the left:

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

We get rid of parentheses

5x^2-3x-23=0

a = 5; b = -3; c = -23;
Δ = b2-4ac
Δ = -32-4·5·(-23)
Δ = 469
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{-(-3)-\sqrt{469}}{2*5}=\frac{3-\sqrt{469}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{469}}{2*5}=\frac{3+\sqrt{469}}{10}
$