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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-51)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+153x-108x-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}
$