X-3/5x=80

Solution for X-3/5x=80 equation:

X-3/5X=80

We move all terms to the left:

X-3/5X-(80)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-80*5X-3=0

Wy multiply elements

5X^2-400X-3=0

a = 5; b = -400; c = -3;
Δ = b2-4ac
Δ = -4002-4·5·(-3)
Δ = 160060
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:

$\sqrt{\Delta}=\sqrt{160060}=\sqrt{4*40015}=\sqrt{4}*\sqrt{40015}=2\sqrt{40015}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2\sqrt{40015}}{2*5}=\frac{400-2\sqrt{40015}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2\sqrt{40015}}{2*5}=\frac{400+2\sqrt{40015}}{10}
$