1/4x-12=16-0.55x

Solution for 1/4x-12=16-0.55x equation:

1/4x-12=16-0.55x

We move all terms to the left:

1/4x-12-(16-0.55x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-0.55x+16)-12=0

We get rid of parentheses

1/4x+0.55x-16-12=0

We multiply all the terms by the denominator


(0.55x)*4x-16*4x-12*4x+1=0

We add all the numbers together, and all the variables

(+0.55x)*4x-16*4x-12*4x+1=0

We multiply parentheses

0x^2-16*4x-12*4x+1=0

Wy multiply elements

0x^2-64x-48x+1=0

We add all the numbers together, and all the variables

x^2-112x+1=0

a = 1; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·1·1
Δ = 12540
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:

$\sqrt{\Delta}=\sqrt{12540}=\sqrt{4*3135}=\sqrt{4}*\sqrt{3135}=2\sqrt{3135}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-2\sqrt{3135}}{2*1}=\frac{112-2\sqrt{3135}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+2\sqrt{3135}}{2*1}=\frac{112+2\sqrt{3135}}{2}
$