6x=7/3x+12=4x+5/2x+3

Solution for 6x=7/3x+12=4x+5/2x+3 equation:

6x=7/3x+12=4x+5/2x+3

We move all terms to the left:

6x-(7/3x+12)=0


Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

6x-7/3x-12=0

We multiply all the terms by the denominator


6x*3x-12*3x-7=0

Wy multiply elements

18x^2-36x-7=0

a = 18; b = -36; c = -7;
Δ = b2-4ac
Δ = -362-4·18·(-7)
Δ = 1800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-30\sqrt{2}}{2*18}=\frac{36-30\sqrt{2}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+30\sqrt{2}}{2*18}=\frac{36+30\sqrt{2}}{36}
$