1/4x-2(x-4)=5

Solution for 1/4x-2(x-4)=5 equation:

1/4x-2(x-4)=5

We move all terms to the left:

1/4x-2(x-4)-(5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply parentheses

1/4x-2x+8-5=0

We multiply all the terms by the denominator


-2x*4x+8*4x-5*4x+1=0

Wy multiply elements

-8x^2+32x-20x+1=0

We add all the numbers together, and all the variables

-8x^2+12x+1=0

a = -8; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-8)·1
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*-8}=\frac{-12-4\sqrt{11}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*-8}=\frac{-12+4\sqrt{11}}{-16}
$