X=910-2/3x

Solution for X=910-2/3x equation:

X=910-2/3X

We move all terms to the left:

X-(910-2/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(-2/3X+910)=0

We get rid of parentheses

X+2/3X-910=0

We multiply all the terms by the denominator


X*3X-910*3X+2=0

Wy multiply elements

3X^2-2730X+2=0

a = 3; b = -2730; c = +2;
Δ = b2-4ac
Δ = -27302-4·3·2
Δ = 7452876
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:

$\sqrt{\Delta}=\sqrt{7452876}=\sqrt{4*1863219}=\sqrt{4}*\sqrt{1863219}=2\sqrt{1863219}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2730)-2\sqrt{1863219}}{2*3}=\frac{2730-2\sqrt{1863219}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2730)+2\sqrt{1863219}}{2*3}=\frac{2730+2\sqrt{1863219}}{6}
$