9993.4+0.42x=0.06x^2

Solution for 9993.4+0.42x=0.06x^2 equation:

9993.4+0.42x=0.06x^2

We move all terms to the left:

9993.4+0.42x-(0.06x^2)=0

We get rid of parentheses

-0.06x^2+0.42x+9993.4=0

a = -0.06; b = 0.42; c = +9993.4;
Δ = b2-4ac
Δ = 0.422-4·(-0.06)·9993.4
Δ = 2398.5924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.42)-\sqrt{2398.5924}}{2*-0.06}=\frac{-0.42-\sqrt{2398.5924}}{-0.12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.42)+\sqrt{2398.5924}}{2*-0.06}=\frac{-0.42+\sqrt{2398.5924}}{-0.12}
$