x/12x+(5x-12)=3x-8

Solution for x/12x+(5x-12)=3x-8 equation:

x/12x+(5x-12)=3x-8

We move all terms to the left:

x/12x+(5x-12)-(3x-8)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We get rid of parentheses

x/12x+5x-3x-12+8=0

We multiply all the terms by the denominator


x+5x*12x-3x*12x-12*12x+8*12x=0

Wy multiply elements

60x^2-36x^2+x-144x+96x=0

We add all the numbers together, and all the variables

24x^2-47x=0

a = 24; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·24·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*24}=\frac{94}{48}
=1+23/24
$