5x+25/8x-72=0

Solution for 5x+25/8x-72=0 equation:

5x+25/8x-72=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


5x*8x-72*8x+25=0

Wy multiply elements

40x^2-576x+25=0

a = 40; b = -576; c = +25;
Δ = b2-4ac
Δ = -5762-4·40·25
Δ = 327776
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:

$\sqrt{\Delta}=\sqrt{327776}=\sqrt{16*20486}=\sqrt{16}*\sqrt{20486}=4\sqrt{20486}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-4\sqrt{20486}}{2*40}=\frac{576-4\sqrt{20486}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+4\sqrt{20486}}{2*40}=\frac{576+4\sqrt{20486}}{80}
$