.75w+8=1/3(w)-7

Solution for .75w+8=1/3(w)-7 equation:

.75w+8=1/3(w)-7

We move all terms to the left:

.75w+8-(1/3(w)-7)=0


Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

.75w-1/3w+7+8=0

We multiply all the terms by the denominator


(.75w)*3w+7*3w+8*3w-1=0

We add all the numbers together, and all the variables

(+.75w)*3w+7*3w+8*3w-1=0

We multiply parentheses

3w^2+7*3w+8*3w-1=0

Wy multiply elements

3w^2+21w+24w-1=0

We add all the numbers together, and all the variables

3w^2+45w-1=0

a = 3; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·3·(-1)
Δ = 2037
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2037}}{2*3}=\frac{-45-\sqrt{2037}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2037}}{2*3}=\frac{-45+\sqrt{2037}}{6}
$