42-x=4/3*x

Solution for 42-x=4/3*x equation:

42-x=4/3x

We move all terms to the left:

42-x-(4/3x)=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-(+4/3x)+42=0

We add all the numbers together, and all the variables

-1x-(+4/3x)+42=0

We get rid of parentheses

-1x-4/3x+42=0

We multiply all the terms by the denominator


-1x*3x+42*3x-4=0

Wy multiply elements

-3x^2+126x-4=0

a = -3; b = 126; c = -4;
Δ = b2-4ac
Δ = 1262-4·(-3)·(-4)
Δ = 15828
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:

$\sqrt{\Delta}=\sqrt{15828}=\sqrt{4*3957}=\sqrt{4}*\sqrt{3957}=2\sqrt{3957}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{3957}}{2*-3}=\frac{-126-2\sqrt{3957}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{3957}}{2*-3}=\frac{-126+2\sqrt{3957}}{-6}
$