8x-21=1/2x+3

Solution for 8x-21=1/2x+3 equation:

8x-21=1/2x+3

We move all terms to the left:

8x-21-(1/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

8x-1/2x-3-21=0

We multiply all the terms by the denominator


8x*2x-3*2x-21*2x-1=0

Wy multiply elements

16x^2-6x-42x-1=0

We add all the numbers together, and all the variables

16x^2-48x-1=0

a = 16; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·16·(-1)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{37}}{2*16}=\frac{48-8\sqrt{37}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{37}}{2*16}=\frac{48+8\sqrt{37}}{32}
$