3/10x-12=3/4x-5

Solution for 3/10x-12=3/4x-5 equation:

3/10x-12=3/4x-5

We move all terms to the left:

3/10x-12-(3/4x-5)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

3/10x-3/4x+5-12=0

We calculate fractions


12x/40x^2+(-30x)/40x^2+5-12=0

We add all the numbers together, and all the variables

12x/40x^2+(-30x)/40x^2-7=0

We multiply all the terms by the denominator


12x+(-30x)-7*40x^2=0

Wy multiply elements

-280x^2+12x+(-30x)=0

We get rid of parentheses

-280x^2+12x-30x=0

We add all the numbers together, and all the variables

-280x^2-18x=0

a = -280; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-280)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-280}=\frac{0}{-560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-280}=\frac{36}{-560}
=-9/140
$