5*3/5w-1/3w+10=4

Solution for 5*3/5w-1/3w+10=4 equation:

5*3/5w-1/3w+10=4

We move all terms to the left:

5*3/5w-1/3w+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

5*3/5w-1/3w+6=0

We calculate fractions


135w/15w^2+(-5w)/15w^2+6=0

We multiply all the terms by the denominator


135w+(-5w)+6*15w^2=0

Wy multiply elements

90w^2+135w+(-5w)=0

We get rid of parentheses

90w^2+135w-5w=0

We add all the numbers together, and all the variables

90w^2+130w=0

a = 90; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·90·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*90}=\frac{-260}{180}
=-1+4/9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*90}=\frac{0}{180}
=0
$