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

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

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

We move all terms to the left:

-7/2w-7/5-(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

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

We calculate fractions


(-875w)/250w^2+(-2w)/250w^2+(-14w)/250w^2+6=0

We multiply all the terms by the denominator


(-875w)+(-2w)+(-14w)+6*250w^2=0

Wy multiply elements

1500w^2+(-875w)+(-2w)+(-14w)=0

We get rid of parentheses

1500w^2-875w-2w-14w=0

We add all the numbers together, and all the variables

1500w^2-891w=0

a = 1500; b = -891; c = 0;
Δ = b2-4ac
Δ = -8912-4·1500·0
Δ = 793881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{793881}=891$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-891)-891}{2*1500}=\frac{0}{3000}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-891)+891}{2*1500}=\frac{1782}{3000}
=297/500
$