X-5/8x=240

Solution for X-5/8x=240 equation:

X-5/8X=240

We move all terms to the left:

X-5/8X-(240)=0


Domain of the equation: 8X!=0

X!=0/8

X!=0

X∈R


We multiply all the terms by the denominator


X*8X-240*8X-5=0

Wy multiply elements

8X^2-1920X-5=0

a = 8; b = -1920; c = -5;
Δ = b2-4ac
Δ = -19202-4·8·(-5)
Δ = 3686560
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:

$\sqrt{\Delta}=\sqrt{3686560}=\sqrt{16*230410}=\sqrt{16}*\sqrt{230410}=4\sqrt{230410}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1920)-4\sqrt{230410}}{2*8}=\frac{1920-4\sqrt{230410}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1920)+4\sqrt{230410}}{2*8}=\frac{1920+4\sqrt{230410}}{16}
$