x=3/2x+16

Solution for x=3/2x+16 equation:

x=3/2x+16

We move all terms to the left:

x-(3/2x+16)=0


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

x-3/2x-16=0

We multiply all the terms by the denominator


x*2x-16*2x-3=0

Wy multiply elements

2x^2-32x-3=0

a = 2; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·2·(-3)
Δ = 1048
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:

$\sqrt{\Delta}=\sqrt{1048}=\sqrt{4*262}=\sqrt{4}*\sqrt{262}=2\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{262}}{2*2}=\frac{32-2\sqrt{262}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{262}}{2*2}=\frac{32+2\sqrt{262}}{4}
$