4/3x-51=-2x-36

Solution for 4/3x-51=-2x-36 equation:

4/3x-51=-2x-36

We move all terms to the left:

4/3x-51-(-2x-36)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x+2x+36-51=0

We multiply all the terms by the denominator


2x*3x+36*3x-51*3x+4=0

Wy multiply elements

6x^2+108x-153x+4=0

We add all the numbers together, and all the variables

6x^2-45x+4=0

a = 6; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·6·4
Δ = 1929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1929}}{2*6}=\frac{45-\sqrt{1929}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1929}}{2*6}=\frac{45+\sqrt{1929}}{12}
$