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

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

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

We move all terms to the left:

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

We multiply all the terms by the denominator


X*2)-((X+1)+(3X+1)+8*2)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2X^2+(3X+1)=0

We get rid of parentheses

2X^2+3X+1=0

a = 2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·2·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-1}{2*2}=\frac{-4}{4}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+1}{2*2}=\frac{-2}{4}
=-1/2
$