6=w(5w+7)

Solution for 6=w(5w+7) equation:

6=w(5w+7)

We move all terms to the left:

6-(w(5w+7))=0


We calculate terms in parentheses: -(w(5w+7)), so:

w(5w+7)

We multiply parentheses

5w^2+7w

Back to the equation:

-(5w^2+7w)


We get rid of parentheses

-5w^2-7w+6=0

a = -5; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-5)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-5}=\frac{-6}{-10}
=3/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-5}=\frac{20}{-10}
=-2
$