4/3x-51=2x+85

Solution for 4/3x-51=2x+85 equation:

4/3x-51=2x+85

We move all terms to the left:

4/3x-51-(2x+85)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-2x-85-51=0

We multiply all the terms by the denominator


-2x*3x-85*3x-51*3x+4=0

Wy multiply elements

-6x^2-255x-153x+4=0

We add all the numbers together, and all the variables

-6x^2-408x+4=0

a = -6; b = -408; c = +4;
Δ = b2-4ac
Δ = -4082-4·(-6)·4
Δ = 166560
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:

$\sqrt{\Delta}=\sqrt{166560}=\sqrt{16*10410}=\sqrt{16}*\sqrt{10410}=4\sqrt{10410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-408)-4\sqrt{10410}}{2*-6}=\frac{408-4\sqrt{10410}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-408)+4\sqrt{10410}}{2*-6}=\frac{408+4\sqrt{10410}}{-12}
$