2/3x-16=-x+10

Solution for 2/3x-16=-x+10 equation:

2/3x-16=-x+10

We move all terms to the left:

2/3x-16-(-x+10)=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+10)-16=0

We get rid of parentheses

2/3x+1x-10-16=0

We multiply all the terms by the denominator


1x*3x-10*3x-16*3x+2=0

Wy multiply elements

3x^2-30x-48x+2=0

We add all the numbers together, and all the variables

3x^2-78x+2=0

a = 3; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·3·2
Δ = 6060
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:

$\sqrt{\Delta}=\sqrt{6060}=\sqrt{4*1515}=\sqrt{4}*\sqrt{1515}=2\sqrt{1515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1515}}{2*3}=\frac{78-2\sqrt{1515}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1515}}{2*3}=\frac{78+2\sqrt{1515}}{6}
$