2/3x-90=144+45x

Solution for 2/3x-90=144+45x equation:

2/3x-90=144+45x

We move all terms to the left:

2/3x-90-(144+45x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(45x+144)-90=0

We get rid of parentheses

2/3x-45x-144-90=0

We multiply all the terms by the denominator


-45x*3x-144*3x-90*3x+2=0

Wy multiply elements

-135x^2-432x-270x+2=0

We add all the numbers together, and all the variables

-135x^2-702x+2=0

a = -135; b = -702; c = +2;
Δ = b2-4ac
Δ = -7022-4·(-135)·2
Δ = 493884
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:

$\sqrt{\Delta}=\sqrt{493884}=\sqrt{36*13719}=\sqrt{36}*\sqrt{13719}=6\sqrt{13719}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-702)-6\sqrt{13719}}{2*-135}=\frac{702-6\sqrt{13719}}{-270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-702)+6\sqrt{13719}}{2*-135}=\frac{702+6\sqrt{13719}}{-270}
$