-7(2w-4)5w=3(w+4)

Solution for -7(2w-4)5w=3(w+4) equation:

-7(2w-4)5w=3(w+4)

We move all terms to the left:

-7(2w-4)5w-(3(w+4))=0

We multiply parentheses

-70w^2+140w-(3(w+4))=0


We calculate terms in parentheses: -(3(w+4)), so:

3(w+4)

We multiply parentheses

3w+12

Back to the equation:

-(3w+12)


We get rid of parentheses

-70w^2+140w-3w-12=0

We add all the numbers together, and all the variables

-70w^2+137w-12=0

a = -70; b = 137; c = -12;
Δ = b2-4ac
Δ = 1372-4·(-70)·(-12)
Δ = 15409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(137)-\sqrt{15409}}{2*-70}=\frac{-137-\sqrt{15409}}{-140}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(137)+\sqrt{15409}}{2*-70}=\frac{-137+\sqrt{15409}}{-140}
$