6w^2=19w-8

Solution for 6w^2=19w-8 equation:

6w^2=19w-8

We move all terms to the left:

6w^2-(19w-8)=0

We get rid of parentheses

6w^2-19w+8=0

a = 6; b = -19; c = +8;
Δ = b2-4ac
Δ = -192-4·6·8
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-13}{2*6}=\frac{6}{12}
=1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+13}{2*6}=\frac{32}{12}
=2+2/3
$