7w2-15w+18=2w2+18w

Solution for 7w2-15w+18=2w2+18w equation:

7w^2-15w+18=2w^2+18w

We move all terms to the left:

7w^2-15w+18-(2w^2+18w)=0

We get rid of parentheses

7w^2-2w^2-15w-18w+18=0

We add all the numbers together, and all the variables

5w^2-33w+18=0

a = 5; b = -33; c = +18;
Δ = b2-4ac
Δ = -332-4·5·18
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-27}{2*5}=\frac{6}{10}
=3/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+27}{2*5}=\frac{60}{10}
=6
$