3/4w+8=w-77

Solution for 3/4w+8=w-77 equation:

3/4w+8=w-77

We move all terms to the left:

3/4w+8-(w-77)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

3/4w-w+77+8=0

We multiply all the terms by the denominator


-w*4w+77*4w+8*4w+3=0

Wy multiply elements

-4w^2+308w+32w+3=0

We add all the numbers together, and all the variables

-4w^2+340w+3=0

a = -4; b = 340; c = +3;
Δ = b2-4ac
Δ = 3402-4·(-4)·3
Δ = 115648
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:

$\sqrt{\Delta}=\sqrt{115648}=\sqrt{64*1807}=\sqrt{64}*\sqrt{1807}=8\sqrt{1807}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-8\sqrt{1807}}{2*-4}=\frac{-340-8\sqrt{1807}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+8\sqrt{1807}}{2*-4}=\frac{-340+8\sqrt{1807}}{-8}
$