5/4w-3/2=-2/3w-7

Solution for 5/4w-3/2=-2/3w-7 equation:

5/4w-3/2=-2/3w-7

We move all terms to the left:

5/4w-3/2-(-2/3w-7)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



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

w∈R


We get rid of parentheses

5/4w+2/3w+7-3/2=0

We calculate fractions


(-108w^2)/48w^2+60w/48w^2+32w/48w^2+7=0

We multiply all the terms by the denominator


(-108w^2)+60w+32w+7*48w^2=0

We add all the numbers together, and all the variables

(-108w^2)+92w+7*48w^2=0

Wy multiply elements

(-108w^2)+336w^2+92w=0

We get rid of parentheses

-108w^2+336w^2+92w=0

We add all the numbers together, and all the variables

228w^2+92w=0

a = 228; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·228·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*228}=\frac{-184}{456}
=-23/57
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*228}=\frac{0}{456}
=0
$