8+2x=-3/2x+1

Solution for 8+2x=-3/2x+1 equation:

8+2x=-3/2x+1

We move all terms to the left:

8+2x-(-3/2x+1)=0


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

2x+3/2x-1+8=0

We multiply all the terms by the denominator


2x*2x-1*2x+8*2x+3=0

Wy multiply elements

4x^2-2x+16x+3=0

We add all the numbers together, and all the variables

4x^2+14x+3=0

a = 4; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·4·3
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{37}}{2*4}=\frac{-14-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{37}}{2*4}=\frac{-14+2\sqrt{37}}{8}
$