-28+6x^2=13x

Solution for -28+6x^2=13x equation:

-28+6x^2=13x

We move all terms to the left:

-28+6x^2-(13x)=0

a = 6; b = -13; c = -28;
Δ = b2-4ac
Δ = -132-4·6·(-28)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*6}=\frac{42}{12}
=3+1/2
$