1/2x+9=8x-24-9x

Solution for 1/2x+9=8x-24-9x equation:

1/2x+9=8x-24-9x

We move all terms to the left:

1/2x+9-(8x-24-9x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x+1x+24+9=0

We multiply all the terms by the denominator


1x*2x+24*2x+9*2x+1=0

Wy multiply elements

2x^2+48x+18x+1=0

We add all the numbers together, and all the variables

2x^2+66x+1=0

a = 2; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·2·1
Δ = 4348
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:

$\sqrt{\Delta}=\sqrt{4348}=\sqrt{4*1087}=\sqrt{4}*\sqrt{1087}=2\sqrt{1087}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1087}}{2*2}=\frac{-66-2\sqrt{1087}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1087}}{2*2}=\frac{-66+2\sqrt{1087}}{4}
$