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 = 4340
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:

$\sqrt{\Delta}=\sqrt{4340}=\sqrt{4*1085}=\sqrt{4}*\sqrt{1085}=2\sqrt{1085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1085}}{2*4}=\frac{66-2\sqrt{1085}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1085}}{2*4}=\frac{66+2\sqrt{1085}}{8}
$