1/2x-12=76+8x

Solution for 1/2x-12=76+8x equation:

1/2x-12=76+8x

We move all terms to the left:

1/2x-12-(76+8x)=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-(8x+76)-12=0

We get rid of parentheses

1/2x-8x-76-12=0

We multiply all the terms by the denominator


-8x*2x-76*2x-12*2x+1=0

Wy multiply elements

-16x^2-152x-24x+1=0

We add all the numbers together, and all the variables

-16x^2-176x+1=0

a = -16; b = -176; c = +1;
Δ = b2-4ac
Δ = -1762-4·(-16)·1
Δ = 31040
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:

$\sqrt{\Delta}=\sqrt{31040}=\sqrt{64*485}=\sqrt{64}*\sqrt{485}=8\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-8\sqrt{485}}{2*-16}=\frac{176-8\sqrt{485}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+8\sqrt{485}}{2*-16}=\frac{176+8\sqrt{485}}{-32}
$