1/2x+12=0.75x-24

Solution for 1/2x+12=0.75x-24 equation:

1/2x+12=0.75x-24

We move all terms to the left:

1/2x+12-(0.75x-24)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-0.75x+24+12=0

We multiply all the terms by the denominator


-(0.75x)*2x+24*2x+12*2x+1=0

We add all the numbers together, and all the variables

-(+0.75x)*2x+24*2x+12*2x+1=0

We multiply parentheses

-0x^2+24*2x+12*2x+1=0

Wy multiply elements

-0x^2+48x+24x+1=0

We add all the numbers together, and all the variables

-1x^2+72x+1=0

a = -1; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-1)·1
Δ = 5188
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:

$\sqrt{\Delta}=\sqrt{5188}=\sqrt{4*1297}=\sqrt{4}*\sqrt{1297}=2\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1297}}{2*-1}=\frac{-72-2\sqrt{1297}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1297}}{2*-1}=\frac{-72+2\sqrt{1297}}{-2}
$