(3/4w)+8=w-7

Solution for (3/4w)+8=w-7 equation:

(3/4w)+8=w-7

We move all terms to the left:

(3/4w)+8-(w-7)=0


Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+3/4w)-(w-7)+8=0

We get rid of parentheses

3/4w-w+7+8=0

We multiply all the terms by the denominator


-w*4w+7*4w+8*4w+3=0

Wy multiply elements

-4w^2+28w+32w+3=0

We add all the numbers together, and all the variables

-4w^2+60w+3=0

a = -4; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-4)·3
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{57}}{2*-4}=\frac{-60-8\sqrt{57}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{57}}{2*-4}=\frac{-60+8\sqrt{57}}{-8}
$