2x+14=3/2x+16

Solution for 2x+14=3/2x+16 equation:

2x+14=3/2x+16

We move all terms to the left:

2x+14-(3/2x+16)=0


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

x∈R


We get rid of parentheses

2x-3/2x-16+14=0

We multiply all the terms by the denominator


2x*2x-16*2x+14*2x-3=0

Wy multiply elements

4x^2-32x+28x-3=0

We add all the numbers together, and all the variables

4x^2-4x-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$