x/10x+5/12=3x-1

Solution for x/10x+5/12=3x-1 equation:

x/10x+5/12=3x-1

We move all terms to the left:

x/10x+5/12-(3x-1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

x/10x-3x+1+5/12=0

We calculate fractions


-3x+12x/120x+50x/120x+1=0

We multiply all the terms by the denominator


-3x*120x+12x+50x+1*120x=0

We add all the numbers together, and all the variables

62x-3x*120x+1*120x=0

Wy multiply elements

-360x^2+62x+120x=0

We add all the numbers together, and all the variables

-360x^2+182x=0

a = -360; b = 182; c = 0;
Δ = b2-4ac
Δ = 1822-4·(-360)·0
Δ = 33124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33124}=182$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(182)-182}{2*-360}=\frac{-364}{-720}
=91/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(182)+182}{2*-360}=\frac{0}{-720}
=0
$