-2/3*x+5=20-x

Solution for -2/3*x+5=20-x equation:

-2/3x+5=20-x

We move all terms to the left:

-2/3x+5-(20-x)=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-(-1x+20)+5=0

We get rid of parentheses

-2/3x+1x-20+5=0

We multiply all the terms by the denominator


1x*3x-20*3x+5*3x-2=0

Wy multiply elements

3x^2-60x+15x-2=0

We add all the numbers together, and all the variables

3x^2-45x-2=0

a = 3; b = -45; c = -2;
Δ = b2-4ac
Δ = -452-4·3·(-2)
Δ = 2049
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{2049}}{2*3}=\frac{45-\sqrt{2049}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*3}=\frac{45+\sqrt{2049}}{6}
$