3/5x-7/10=-4+7/15x

Solution for 3/5x-7/10=-4+7/15x equation:

3/5x-7/10=-4+7/15x

We move all terms to the left:

3/5x-7/10-(-4+7/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(7/15x-4)-7/10=0

We get rid of parentheses

3/5x-7/15x+4-7/10=0

We calculate fractions


(-525x^2)/750x^2+450x/750x^2+(-350x)/750x^2+4=0

We multiply all the terms by the denominator


(-525x^2)+450x+(-350x)+4*750x^2=0

Wy multiply elements

(-525x^2)+3000x^2+450x+(-350x)=0

We get rid of parentheses

-525x^2+3000x^2+450x-350x=0

We add all the numbers together, and all the variables

2475x^2+100x=0

a = 2475; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·2475·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*2475}=\frac{-200}{4950}
=-4/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*2475}=\frac{0}{4950}
=0
$