3w^2=7w-2

Solution for 3w^2=7w-2 equation:

3w^2=7w-2

We move all terms to the left:

3w^2-(7w-2)=0

We get rid of parentheses

3w^2-7w+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$