21/2x-7=8+x

Solution for 21/2x-7=8+x equation:

21/2x-7=8+x

We move all terms to the left:

21/2x-7-(8+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

21/2x-(x+8)-7=0

We get rid of parentheses

21/2x-x-8-7=0

We multiply all the terms by the denominator


-x*2x-8*2x-7*2x+21=0

Wy multiply elements

-2x^2-16x-14x+21=0

We add all the numbers together, and all the variables

-2x^2-30x+21=0

a = -2; b = -30; c = +21;
Δ = b2-4ac
Δ = -302-4·(-2)·21
Δ = 1068
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:

$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{267}}{2*-2}=\frac{30-2\sqrt{267}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{267}}{2*-2}=\frac{30+2\sqrt{267}}{-4}
$