X(10x-1)=3

Solution for X(10x-1)=3 equation:

X(10X-1)=3

We move all terms to the left:

X(10X-1)-(3)=0

We multiply parentheses

10X^2-1X-3=0

a = 10; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·10·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*10}=\frac{-10}{20}
=-1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*10}=\frac{12}{20}
=3/5
$