X/625x+2=(5)2x+10

Solution for X/625x+2=(5)2x+10 equation:

X/625X+2=(5)2X+10

We move all terms to the left:

X/625X+2-((5)2X+10)=0


Domain of the equation: 625X!=0

X!=0/625

X!=0

X∈R


We get rid of parentheses

X/625X-52X-10+2=0

We multiply all the terms by the denominator


X-52X*625X-10*625X+2*625X=0

Wy multiply elements

-32500X^2+X-6250X+1250X=0

We add all the numbers together, and all the variables

-32500X^2-4999X=0

a = -32500; b = -4999; c = 0;
Δ = b2-4ac
Δ = -49992-4·(-32500)·0
Δ = 24990001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24990001}=4999$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4999)-4999}{2*-32500}=\frac{0}{-65000}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4999)+4999}{2*-32500}=\frac{9998}{-65000}
=-4999/32500
$