3/4w-7/10w-7=30

Solution for 3/4w-7/10w-7=30 equation:

3/4w-7/10w-7=30

We move all terms to the left:

3/4w-7/10w-7-(30)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R


We add all the numbers together, and all the variables

3/4w-7/10w-37=0

We calculate fractions


30w/40w^2+(-28w)/40w^2-37=0

We multiply all the terms by the denominator


30w+(-28w)-37*40w^2=0

Wy multiply elements

-1480w^2+30w+(-28w)=0

We get rid of parentheses

-1480w^2+30w-28w=0

We add all the numbers together, and all the variables

-1480w^2+2w=0

a = -1480; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-1480)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-1480}=\frac{-4}{-2960}
=1/740
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-1480}=\frac{0}{-2960}
=0
$