2(w+3)-10=6(32-3w);w=

Solution for 2(w+3)-10=6(32-3w);w= equation:

2(w+3)-10=6(32-3w)w=

We move all terms to the left:

2(w+3)-10-(6(32-3w)w)=0

We add all the numbers together, and all the variables

2(w+3)-(6(-3w+32)w)-10=0

We multiply parentheses

2w-(6(-3w+32)w)+6-10=0


We calculate terms in parentheses: -(6(-3w+32)w), so:

6(-3w+32)w

We multiply parentheses

-18w^2+192w

Back to the equation:

-(-18w^2+192w)


We add all the numbers together, and all the variables

-(-18w^2+192w)+2w-4=0

We get rid of parentheses

18w^2-192w+2w-4=0

We add all the numbers together, and all the variables

18w^2-190w-4=0

a = 18; b = -190; c = -4;
Δ = b2-4ac
Δ = -1902-4·18·(-4)
Δ = 36388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36388}=\sqrt{4*9097}=\sqrt{4}*\sqrt{9097}=2\sqrt{9097}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{9097}}{2*18}=\frac{190-2\sqrt{9097}}{36}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{9097}}{2*18}=\frac{190+2\sqrt{9097}}{36}
$