48+90-x=2/3x-180

Solution for 48+90-x=2/3x-180 equation:

48+90-x=2/3x-180

We move all terms to the left:

48+90-x-(2/3x-180)=0


Domain of the equation: 3x-180)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(2/3x-180)+138=0

We get rid of parentheses

-1x-2/3x+180+138=0

We multiply all the terms by the denominator


-1x*3x+180*3x+138*3x-2=0

Wy multiply elements

-3x^2+540x+414x-2=0

We add all the numbers together, and all the variables

-3x^2+954x-2=0

a = -3; b = 954; c = -2;
Δ = b2-4ac
Δ = 9542-4·(-3)·(-2)
Δ = 910092
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:

$\sqrt{\Delta}=\sqrt{910092}=\sqrt{4*227523}=\sqrt{4}*\sqrt{227523}=2\sqrt{227523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(954)-2\sqrt{227523}}{2*-3}=\frac{-954-2\sqrt{227523}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(954)+2\sqrt{227523}}{2*-3}=\frac{-954+2\sqrt{227523}}{-6}
$