6x^2=13x+8

Solution for 6x^2=13x+8 equation:

6x^2=13x+8

We move all terms to the left:

6x^2-(13x+8)=0

We get rid of parentheses

6x^2-13x-8=0

a = 6; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·6·(-8)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*6}=\frac{32}{12}
=2+2/3
$