-3(2w+5)7w=5(w-11)

Solution for -3(2w+5)7w=5(w-11) equation:

-3(2w+5)7w=5(w-11)

We move all terms to the left:

-3(2w+5)7w-(5(w-11))=0

We multiply parentheses

-42w^2-105w-(5(w-11))=0


We calculate terms in parentheses: -(5(w-11)), so:

5(w-11)

We multiply parentheses

5w-55

Back to the equation:

-(5w-55)


We get rid of parentheses

-42w^2-105w-5w+55=0

We add all the numbers together, and all the variables

-42w^2-110w+55=0

a = -42; b = -110; c = +55;
Δ = b2-4ac
Δ = -1102-4·(-42)·55
Δ = 21340
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:

$\sqrt{\Delta}=\sqrt{21340}=\sqrt{4*5335}=\sqrt{4}*\sqrt{5335}=2\sqrt{5335}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{5335}}{2*-42}=\frac{110-2\sqrt{5335}}{-84}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{5335}}{2*-42}=\frac{110+2\sqrt{5335}}{-84}
$