4w^2-11w=w-4

Solution for 4w^2-11w=w-4 equation:

4w^2-11w=w-4

We move all terms to the left:

4w^2-11w-(w-4)=0

We get rid of parentheses

4w^2-11w-w+4=0

We add all the numbers together, and all the variables

4w^2-12w+4=0

a = 4; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·4·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{5}}{2*4}=\frac{12-4\sqrt{5}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{5}}{2*4}=\frac{12+4\sqrt{5}}{8}
$