3/2x+5=8x+6

Solution for 3/2x+5=8x+6 equation:

3/2x+5=8x+6

We move all terms to the left:

3/2x+5-(8x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-8x-6+5=0

We multiply all the terms by the denominator


-8x*2x-6*2x+5*2x+3=0

Wy multiply elements

-16x^2-12x+10x+3=0

We add all the numbers together, and all the variables

-16x^2-2x+3=0

a = -16; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-16)·3
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*-16}=\frac{-12}{-32}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-16}=\frac{16}{-32}
=-1/2
$