393x=0.9x^2

Solution for 393x=0.9x^2 equation:

393x=0.9x^2

We move all terms to the left:

393x-(0.9x^2)=0

We get rid of parentheses

-0.9x^2+393x=0

a = -0.9; b = 393; c = 0;
Δ = b2-4ac
Δ = 3932-4·(-0.9)·0
Δ = 154449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{154449}=393$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(393)-393}{2*-0.9}=\frac{-786}{-1.8}
=436+1/1.5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(393)+393}{2*-0.9}=\frac{0}{-1.8}
=0
$