8/5x-x=51

Solution for 8/5x-x=51 equation:

8/5x-x=51

We move all terms to the left:

8/5x-x-(51)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/5x-51=0

We multiply all the terms by the denominator


-1x*5x-51*5x+8=0

Wy multiply elements

-5x^2-255x+8=0

a = -5; b = -255; c = +8;
Δ = b2-4ac
Δ = -2552-4·(-5)·8
Δ = 65185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-\sqrt{65185}}{2*-5}=\frac{255-\sqrt{65185}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+\sqrt{65185}}{2*-5}=\frac{255+\sqrt{65185}}{-10}
$