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

Solution for 2.8(x-5)=1/4x-4 equation:

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

We move all terms to the left:

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


Domain of the equation: 4x-4)!=0

x∈R


We multiply parentheses

2.8x-(1/4x-4)-14=0

We get rid of parentheses

2.8x-1/4x+4-14=0

We multiply all the terms by the denominator


(2.8x)*4x+4*4x-14*4x-1=0

We add all the numbers together, and all the variables

(+2.8x)*4x+4*4x-14*4x-1=0

We multiply parentheses

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

Wy multiply elements

8x^2+16x-56x-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}
$