64=(2w-10)w

Solution for 64=(2w-10)w equation:

64=(2w-10)w

We move all terms to the left:

64-((2w-10)w)=0


We calculate terms in parentheses: -((2w-10)w), so:

(2w-10)w

We multiply parentheses

2w^2-10w

Back to the equation:

-(2w^2-10w)


We get rid of parentheses

-2w^2+10w+64=0

a = -2; b = 10; c = +64;
Δ = b2-4ac
Δ = 102-4·(-2)·64
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{17}}{2*-2}=\frac{-10-6\sqrt{17}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{17}}{2*-2}=\frac{-10+6\sqrt{17}}{-4}
$