21/2x+3=8+2x

Solution for 21/2x+3=8+2x equation:

21/2x+3=8+2x

We move all terms to the left:

21/2x+3-(8+2x)=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-(2x+8)+3=0

We get rid of parentheses

21/2x-2x-8+3=0

We multiply all the terms by the denominator


-2x*2x-8*2x+3*2x+21=0

Wy multiply elements

-4x^2-16x+6x+21=0

We add all the numbers together, and all the variables

-4x^2-10x+21=0

a = -4; b = -10; c = +21;
Δ = b2-4ac
Δ = -102-4·(-4)·21
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{109}}{2*-4}=\frac{10-2\sqrt{109}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{109}}{2*-4}=\frac{10+2\sqrt{109}}{-8}
$