1/5x+10=2/3x-7

Solution for 1/5x+10=2/3x-7 equation:

1/5x+10=2/3x-7

We move all terms to the left:

1/5x+10-(2/3x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

1/5x-2/3x+7+10=0

We calculate fractions


3x/15x^2+(-10x)/15x^2+7+10=0

We add all the numbers together, and all the variables

3x/15x^2+(-10x)/15x^2+17=0

We multiply all the terms by the denominator


3x+(-10x)+17*15x^2=0

Wy multiply elements

255x^2+3x+(-10x)=0

We get rid of parentheses

255x^2+3x-10x=0

We add all the numbers together, and all the variables

255x^2-7x=0

a = 255; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·255·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*255}=\frac{0}{510}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*255}=\frac{14}{510}
=7/255
$