3x=1/25x+12

Solution for 3x=1/25x+12 equation:

3x=1/25x+12

We move all terms to the left:

3x-(1/25x+12)=0


Domain of the equation: 25x+12)!=0

x∈R


We get rid of parentheses

3x-1/25x-12=0

We multiply all the terms by the denominator


3x*25x-12*25x-1=0

Wy multiply elements

75x^2-300x-1=0

a = 75; b = -300; c = -1;
Δ = b2-4ac
Δ = -3002-4·75·(-1)
Δ = 90300
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:

$\sqrt{\Delta}=\sqrt{90300}=\sqrt{100*903}=\sqrt{100}*\sqrt{903}=10\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-10\sqrt{903}}{2*75}=\frac{300-10\sqrt{903}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+10\sqrt{903}}{2*75}=\frac{300+10\sqrt{903}}{150}
$