x=4/3x-16

Solution for x=4/3x-16 equation:

x=4/3x-16

We move all terms to the left:

x-(4/3x-16)=0


Domain of the equation: 3x-16)!=0

x∈R


We get rid of parentheses

x-4/3x+16=0

We multiply all the terms by the denominator


x*3x+16*3x-4=0

Wy multiply elements

3x^2+48x-4=0

a = 3; b = 48; c = -4;
Δ = b2-4ac
Δ = 482-4·3·(-4)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{3}}{2*3}=\frac{-48-28\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{3}}{2*3}=\frac{-48+28\sqrt{3}}{6}
$