3/5w+10=4+2/3w

Solution for 3/5w+10=4+2/3w equation:

3/5w+10=4+2/3w

We move all terms to the left:

3/5w+10-(4+2/3w)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

3/5w-(2/3w+4)+10=0

We get rid of parentheses

3/5w-2/3w-4+10=0

We calculate fractions


9w/15w^2+(-10w)/15w^2-4+10=0

We add all the numbers together, and all the variables

9w/15w^2+(-10w)/15w^2+6=0

We multiply all the terms by the denominator


9w+(-10w)+6*15w^2=0

Wy multiply elements

90w^2+9w+(-10w)=0

We get rid of parentheses

90w^2+9w-10w=0

We add all the numbers together, and all the variables

90w^2-1w=0

a = 90; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·90·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*90}=\frac{0}{180}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*90}=\frac{2}{180}
=1/90
$