9+3(2w-3)=-3(6w-5)6w

Solution for 9+3(2w-3)=-3(6w-5)6w equation:

9+3(2w-3)=-3(6w-5)6w

We move all terms to the left:

9+3(2w-3)-(-3(6w-5)6w)=0

We multiply parentheses

6w-(-3(6w-5)6w)-9+9=0


We calculate terms in parentheses: -(-3(6w-5)6w), so:

-3(6w-5)6w

We multiply parentheses

-108w^2+90w

Back to the equation:

-(-108w^2+90w)


We add all the numbers together, and all the variables

-(-108w^2+90w)+6w=0

We get rid of parentheses

108w^2-90w+6w=0

We add all the numbers together, and all the variables

108w^2-84w=0

a = 108; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·108·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*108}=\frac{0}{216}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*108}=\frac{168}{216}
=7/9
$