1/4w+5=2w-2

Solution for 1/4w+5=2w-2 equation:

1/4w+5=2w-2

We move all terms to the left:

1/4w+5-(2w-2)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

1/4w-2w+2+5=0

We multiply all the terms by the denominator


-2w*4w+2*4w+5*4w+1=0

Wy multiply elements

-8w^2+8w+20w+1=0

We add all the numbers together, and all the variables

-8w^2+28w+1=0

a = -8; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-8)·1
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*-8}=\frac{-28-4\sqrt{51}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*-8}=\frac{-28+4\sqrt{51}}{-16}
$