-3/2w-7/2=1/5w-6

Solution for -3/2w-7/2=1/5w-6 equation:

-3/2w-7/2=1/5w-6

We move all terms to the left:

-3/2w-7/2-(1/5w-6)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 5w-6)!=0

w∈R


We get rid of parentheses

-3/2w-1/5w+6-7/2=0

We calculate fractions


(-15w)/40w^2+(-8w)/40w^2+(-35w)/40w^2+6=0

We multiply all the terms by the denominator


(-15w)+(-8w)+(-35w)+6*40w^2=0

Wy multiply elements

240w^2+(-15w)+(-8w)+(-35w)=0

We get rid of parentheses

240w^2-15w-8w-35w=0

We add all the numbers together, and all the variables

240w^2-58w=0

a = 240; b = -58; c = 0;
Δ = b2-4ac
Δ = -582-4·240·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-58}{2*240}=\frac{0}{480}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+58}{2*240}=\frac{116}{480}
=29/120
$