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

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

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

We move all terms to the left:

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


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

3/5w+2/3w+6=0

We calculate fractions


9w/15w^2+10w/15w^2+6=0

We multiply all the terms by the denominator


9w+10w+6*15w^2=0

We add all the numbers together, and all the variables

19w+6*15w^2=0

Wy multiply elements

90w^2+19w=0

a = 90; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·90·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*90}=\frac{-38}{180}
=-19/90
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*90}=\frac{0}{180}
=0
$