0.5x+4=1/4x+12

Solution for 0.5x+4=1/4x+12 equation:

0.5x+4=1/4x+12

We move all terms to the left:

0.5x+4-(1/4x+12)=0


Domain of the equation: 4x+12)!=0

x∈R


We get rid of parentheses

0.5x-1/4x-12+4=0

We multiply all the terms by the denominator


(0.5x)*4x-12*4x+4*4x-1=0

We add all the numbers together, and all the variables

(+0.5x)*4x-12*4x+4*4x-1=0

We multiply parentheses

0x^2-12*4x+4*4x-1=0

Wy multiply elements

0x^2-48x+16x-1=0

We add all the numbers together, and all the variables

x^2-32x-1=0

a = 1; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·1·(-1)
Δ = 1028
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:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{257}}{2*1}=\frac{32-2\sqrt{257}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{257}}{2*1}=\frac{32+2\sqrt{257}}{2}
$