13w-2w(4w+1)=w-58

Solution for 13w-2w(4w+1)=w-58 equation:

13w-2w(4w+1)=w-58

We move all terms to the left:

13w-2w(4w+1)-(w-58)=0

We multiply parentheses

-8w^2+13w-2w-(w-58)=0

We get rid of parentheses

-8w^2+13w-2w-w+58=0

We add all the numbers together, and all the variables

-8w^2+10w+58=0

a = -8; b = 10; c = +58;
Δ = b2-4ac
Δ = 102-4·(-8)·58
Δ = 1956
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:

$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{489}}{2*-8}=\frac{-10-2\sqrt{489}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{489}}{2*-8}=\frac{-10+2\sqrt{489}}{-16}
$