5w+7/4w-12=w

Solution for 5w+7/4w-12=w equation:

5w+7/4w-12=w

We move all terms to the left:

5w+7/4w-12-(w)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

4w+7/4w-12=0

We multiply all the terms by the denominator


4w*4w-12*4w+7=0

Wy multiply elements

16w^2-48w+7=0

a = 16; b = -48; c = +7;
Δ = b2-4ac
Δ = -482-4·16·7
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{29}}{2*16}=\frac{48-8\sqrt{29}}{32}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{29}}{2*16}=\frac{48+8\sqrt{29}}{32}
$