13x-6x^2=6

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

13x-6x^2=6

We move all terms to the left:

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

a = -6; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·(-6)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-6}=\frac{-8}{-12}
=2/3
$