3/2(1x)+6+1/2(1x)=15+2x

Solution for 3/2(1x)+6+1/2(1x)=15+2x equation:

3/2(1x)+6+1/2(1x)=15+2x

We move all terms to the left:

3/2(1x)+6+1/2(1x)-(15+2x)=0


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We add all the numbers together, and all the variables

3/21x+1/21x-(2x+15)+6=0

We get rid of parentheses

3/21x+1/21x-2x-15+6=0

We multiply all the terms by the denominator


-2x*21x-15*21x+6*21x+3+1=0

We add all the numbers together, and all the variables

-2x*21x-15*21x+6*21x+4=0

Wy multiply elements

-42x^2-315x+126x+4=0

We add all the numbers together, and all the variables

-42x^2-189x+4=0

a = -42; b = -189; c = +4;
Δ = b2-4ac
Δ = -1892-4·(-42)·4
Δ = 36393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-\sqrt{36393}}{2*-42}=\frac{189-\sqrt{36393}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+\sqrt{36393}}{2*-42}=\frac{189+\sqrt{36393}}{-84}
$