5x+25/8x-72=1

Solution for 5x+25/8x-72=1 equation:

5x+25/8x-72=1

We move all terms to the left:

5x+25/8x-72-(1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5x+25/8x-73=0

We multiply all the terms by the denominator


5x*8x-73*8x+25=0

Wy multiply elements

40x^2-584x+25=0

a = 40; b = -584; c = +25;
Δ = b2-4ac
Δ = -5842-4·40·25
Δ = 337056
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:

$\sqrt{\Delta}=\sqrt{337056}=\sqrt{16*21066}=\sqrt{16}*\sqrt{21066}=4\sqrt{21066}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-584)-4\sqrt{21066}}{2*40}=\frac{584-4\sqrt{21066}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-584)+4\sqrt{21066}}{2*40}=\frac{584+4\sqrt{21066}}{80}
$