5/6x+4=3/8x+12

Solution for 5/6x+4=3/8x+12 equation:

5/6x+4=3/8x+12

We move all terms to the left:

5/6x+4-(3/8x+12)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x+12)!=0

x∈R


We get rid of parentheses

5/6x-3/8x-12+4=0

We calculate fractions


40x/48x^2+(-18x)/48x^2-12+4=0

We add all the numbers together, and all the variables

40x/48x^2+(-18x)/48x^2-8=0

We multiply all the terms by the denominator


40x+(-18x)-8*48x^2=0

Wy multiply elements

-384x^2+40x+(-18x)=0

We get rid of parentheses

-384x^2+40x-18x=0

We add all the numbers together, and all the variables

-384x^2+22x=0

a = -384; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-384)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-384}=\frac{-44}{-768}
=11/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-384}=\frac{0}{-768}
=0
$