2/3x+x=12.5

Solution for 2/3x+x=12.5 equation:

2/3x+x=12.5

We move all terms to the left:

2/3x+x-(12.5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-12.5=0

We multiply all the terms by the denominator


x*3x-(12.5)*3x+2=0

We multiply parentheses

x*3x-37.5x+2=0

Wy multiply elements

3x^2-37.5x+2=0

a = 3; b = -37.5; c = +2;
Δ = b2-4ac
Δ = -37.52-4·3·2
Δ = 1382.25
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{-(-37.5)-\sqrt{1382.25}}{2*3}=\frac{37.5-\sqrt{1382.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37.5)+\sqrt{1382.25}}{2*3}=\frac{37.5+\sqrt{1382.25}}{6}
$