6+X=7+3/2x

Solution for 6+X=7+3/2x equation:

6+X=7+3/2X

We move all terms to the left:

6+X-(7+3/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(3/2X+7)+6=0

We get rid of parentheses

X-3/2X-7+6=0

We multiply all the terms by the denominator


X*2X-7*2X+6*2X-3=0

Wy multiply elements

2X^2-14X+12X-3=0

We add all the numbers together, and all the variables

2X^2-2X-3=0

a = 2; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·2·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*2}=\frac{2-2\sqrt{7}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*2}=\frac{2+2\sqrt{7}}{4}
$