1/2x+16=3x-12

Solution for 1/2x+16=3x-12 equation:

1/2x+16=3x-12

We move all terms to the left:

1/2x+16-(3x-12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3x+12+16=0

We multiply all the terms by the denominator


-3x*2x+12*2x+16*2x+1=0

Wy multiply elements

-6x^2+24x+32x+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 = 3160
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:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{790}}{2*-6}=\frac{-56-2\sqrt{790}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{790}}{2*-6}=\frac{-56+2\sqrt{790}}{-12}
$