2X-9=1/2x+24

Solution for 2X-9=1/2x+24 equation:

2X-9=1/2X+24

We move all terms to the left:

2X-9-(1/2X+24)=0


Domain of the equation: 2X+24)!=0

X∈R


We get rid of parentheses

2X-1/2X-24-9=0

We multiply all the terms by the denominator


2X*2X-24*2X-9*2X-1=0

Wy multiply elements

4X^2-48X-18X-1=0

We add all the numbers together, and all the variables

4X^2-66X-1=0

a = 4; b = -66; c = -1;
Δ = b2-4ac
Δ = -662-4·4·(-1)
Δ = 4372
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:

$\sqrt{\Delta}=\sqrt{4372}=\sqrt{4*1093}=\sqrt{4}*\sqrt{1093}=2\sqrt{1093}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1093}}{2*4}=\frac{66-2\sqrt{1093}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1093}}{2*4}=\frac{66+2\sqrt{1093}}{8}
$