23=3x^2-15x

Solution for 23=3x^2-15x equation:

23=3x^2-15x

We move all terms to the left:

23-(3x^2-15x)=0

We get rid of parentheses

-3x^2+15x+23=0

a = -3; b = 15; c = +23;
Δ = b2-4ac
Δ = 152-4·(-3)·23
Δ = 501
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{-(15)-\sqrt{501}}{2*-3}=\frac{-15-\sqrt{501}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{501}}{2*-3}=\frac{-15+\sqrt{501}}{-6}
$