-x+9=4/3x-5

Solution for -x+9=4/3x-5 equation:

-x+9=4/3x-5

We move all terms to the left:

-x+9-(4/3x-5)=0


Domain of the equation: 3x-5)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(4/3x-5)+9=0

We get rid of parentheses

-1x-4/3x+5+9=0

We multiply all the terms by the denominator


-1x*3x+5*3x+9*3x-4=0

Wy multiply elements

-3x^2+15x+27x-4=0

We add all the numbers together, and all the variables

-3x^2+42x-4=0

a = -3; b = 42; c = -4;
Δ = b2-4ac
Δ = 422-4·(-3)·(-4)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{429}}{2*-3}=\frac{-42-2\sqrt{429}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{429}}{2*-3}=\frac{-42+2\sqrt{429}}{-6}
$