3/4w+8=w-1

Solution for 3/4w+8=w-1 equation:

3/4w+8=w-1

We move all terms to the left:

3/4w+8-(w-1)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

3/4w-w+1+8=0

We multiply all the terms by the denominator


-w*4w+1*4w+8*4w+3=0

Wy multiply elements

-4w^2+4w+32w+3=0

We add all the numbers together, and all the variables

-4w^2+36w+3=0

a = -4; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-4)·3
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{21}}{2*-4}=\frac{-36-8\sqrt{21}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{21}}{2*-4}=\frac{-36+8\sqrt{21}}{-8}
$