X=111/3x-9=14x-7-13x

Solution for X=111/3x-9=14x-7-13x equation:

X=111/3X-9=14X-7-13X

We move all terms to the left:

X-(111/3X-9)=0


Domain of the equation: 3X-9)!=0

X∈R


We get rid of parentheses

X-111/3X+9=0

We multiply all the terms by the denominator


X*3X+9*3X-111=0

Wy multiply elements

3X^2+27X-111=0

a = 3; b = 27; c = -111;
Δ = b2-4ac
Δ = 272-4·3·(-111)
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{229}}{2*3}=\frac{-27-3\sqrt{229}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{229}}{2*3}=\frac{-27+3\sqrt{229}}{6}
$