14x=42x^2

Solution for 14x=42x^2 equation:

14x=42x^2

We move all terms to the left:

14x-(42x^2)=0

determiningTheFunctionDomain
-42x^2+14x=0

a = -42; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-42)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-42}=\frac{-28}{-84}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-42}=\frac{0}{-84}
=0
$