-4x+24=3+1/2x

Solution for -4x+24=3+1/2x equation:

-4x+24=3+1/2x

We move all terms to the left:

-4x+24-(3+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(1/2x+3)+24=0

We get rid of parentheses

-4x-1/2x-3+24=0

We multiply all the terms by the denominator


-4x*2x-3*2x+24*2x-1=0

Wy multiply elements

-8x^2-6x+48x-1=0

We add all the numbers together, and all the variables

-8x^2+42x-1=0

a = -8; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·(-8)·(-1)
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{433}}{2*-8}=\frac{-42-2\sqrt{433}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{433}}{2*-8}=\frac{-42+2\sqrt{433}}{-16}
$