1/5x-4=3/10x-7

Solution for 1/5x-4=3/10x-7 equation:

1/5x-4=3/10x-7

We move all terms to the left:

1/5x-4-(3/10x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-7)!=0

x∈R


We get rid of parentheses

1/5x-3/10x+7-4=0

We calculate fractions


10x/50x^2+(-15x)/50x^2+7-4=0

We add all the numbers together, and all the variables

10x/50x^2+(-15x)/50x^2+3=0

We multiply all the terms by the denominator


10x+(-15x)+3*50x^2=0

Wy multiply elements

150x^2+10x+(-15x)=0

We get rid of parentheses

150x^2+10x-15x=0

We add all the numbers together, and all the variables

150x^2-5x=0

a = 150; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·150·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*150}=\frac{10}{300}
=1/30
$