4=3x^2-13x

Solution for 4=3x^2-13x equation:

4=3x^2-13x

We move all terms to the left:

4-(3x^2-13x)=0

We get rid of parentheses

-3x^2+13x+4=0

a = -3; b = 13; c = +4;
Δ = b2-4ac
Δ = 132-4·(-3)·4
Δ = 217
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{-(13)-\sqrt{217}}{2*-3}=\frac{-13-\sqrt{217}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{217}}{2*-3}=\frac{-13+\sqrt{217}}{-6}
$