4/5x-x=-64+8

Solution for 4/5x-x=-64+8 equation:

4/5x-x=-64+8

We move all terms to the left:

4/5x-x-(-64+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-x-(-56)=0

We add all the numbers together, and all the variables

-1x+4/5x+56=0

We multiply all the terms by the denominator


-1x*5x+56*5x+4=0

Wy multiply elements

-5x^2+280x+4=0

a = -5; b = 280; c = +4;
Δ = b2-4ac
Δ = 2802-4·(-5)·4
Δ = 78480
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:

$\sqrt{\Delta}=\sqrt{78480}=\sqrt{144*545}=\sqrt{144}*\sqrt{545}=12\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-12\sqrt{545}}{2*-5}=\frac{-280-12\sqrt{545}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+12\sqrt{545}}{2*-5}=\frac{-280+12\sqrt{545}}{-10}
$