77=w(3w-10)

Solution for 77=w(3w-10) equation:

77=w(3w-10)

We move all terms to the left:

77-(w(3w-10))=0


We calculate terms in parentheses: -(w(3w-10)), so:

w(3w-10)

We multiply parentheses

3w^2-10w

Back to the equation:

-(3w^2-10w)


We get rid of parentheses

-3w^2+10w+77=0

a = -3; b = 10; c = +77;
Δ = b2-4ac
Δ = 102-4·(-3)·77
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-32}{2*-3}=\frac{-42}{-6}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+32}{2*-3}=\frac{22}{-6}
=-3+2/3
$