6w^2=7w-2

Solution for 6w^2=7w-2 equation:

6w^2=7w-2

We move all terms to the left:

6w^2-(7w-2)=0

We get rid of parentheses

6w^2-7w+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$