X-29=2/3x-10.6

Solution for X-29=2/3x-10.6 equation:

X-29=2/3X-10.6

We move all terms to the left:

X-29-(2/3X-10.6)=0


Domain of the equation: 3X-10.6)!=0

X∈R


We get rid of parentheses

X-2/3X+10.6-29=0

We multiply all the terms by the denominator


X*3X+(10.6)*3X-29*3X-2=0

We multiply parentheses

X*3X+31.8X-29*3X-2=0

Wy multiply elements

3X^2+31.8X-87X-2=0

We add all the numbers together, and all the variables

3X^2-55.2X-2=0

a = 3; b = -55.2; c = -2;
Δ = b2-4ac
Δ = -55.22-4·3·(-2)
Δ = 3071.04
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{-(-55.2)-\sqrt{3071.04}}{2*3}=\frac{55.2-\sqrt{3071.04}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55.2)+\sqrt{3071.04}}{2*3}=\frac{55.2+\sqrt{3071.04}}{6}
$