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

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

X+1=3/2X+3=8

We move all terms to the left:

X+1-(3/2X+3)=0


Domain of the equation: 2X+3)!=0

X∈R


We get rid of parentheses

X-3/2X-3+1=0

We multiply all the terms by the denominator


X*2X-3*2X+1*2X-3=0

Wy multiply elements

2X^2-6X+2X-3=0

We add all the numbers together, and all the variables

2X^2-4X-3=0

a = 2; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*2}=\frac{4-2\sqrt{10}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*2}=\frac{4+2\sqrt{10}}{4}
$