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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2+56x-1=0

a = -6; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·(-6)·(-1)
Δ = 3112
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:

$\sqrt{\Delta}=\sqrt{3112}=\sqrt{4*778}=\sqrt{4}*\sqrt{778}=2\sqrt{778}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{778}}{2*-6}=\frac{-56-2\sqrt{778}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{778}}{2*-6}=\frac{-56+2\sqrt{778}}{-12}
$