5/8x+25=10x

Solution for 5/8x+25=10x equation:

5/8x+25=10x

We move all terms to the left:

5/8x+25-(10x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+5/8x+25=0

We multiply all the terms by the denominator


-10x*8x+25*8x+5=0

Wy multiply elements

-80x^2+200x+5=0

a = -80; b = 200; c = +5;
Δ = b2-4ac
Δ = 2002-4·(-80)·5
Δ = 41600
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:

$\sqrt{\Delta}=\sqrt{41600}=\sqrt{1600*26}=\sqrt{1600}*\sqrt{26}=40\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{26}}{2*-80}=\frac{-200-40\sqrt{26}}{-160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{26}}{2*-80}=\frac{-200+40\sqrt{26}}{-160}
$