1/4x+4=14+2.75x

Solution for 1/4x+4=14+2.75x equation:

1/4x+4=14+2.75x

We move all terms to the left:

1/4x+4-(14+2.75x)=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-(2.75x+14)+4=0

We get rid of parentheses

1/4x-2.75x-14+4=0

We multiply all the terms by the denominator


-(2.75x)*4x-14*4x+4*4x+1=0

We add all the numbers together, and all the variables

-(+2.75x)*4x-14*4x+4*4x+1=0

We multiply parentheses

-8x^2-14*4x+4*4x+1=0

Wy multiply elements

-8x^2-56x+16x+1=0

We add all the numbers together, and all the variables

-8x^2-40x+1=0

a = -8; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·(-8)·1
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{102}}{2*-8}=\frac{40-4\sqrt{102}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{102}}{2*-8}=\frac{40+4\sqrt{102}}{-16}
$