0.4x^2+6x=0.9x^2

Solution for 0.4x^2+6x=0.9x^2 equation:

0.4x^2+6x=0.9x^2

We move all terms to the left:

0.4x^2+6x-(0.9x^2)=0

We get rid of parentheses

0.4x^2-0.9x^2+6x=0

We add all the numbers together, and all the variables

-0.5x^2+6x=0

a = -0.5; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-0.5)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-0.5}=\frac{-12}{-1}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-0.5}=\frac{0}{-1}
=0
$