0,9x2=5,4x

Solution for 0,9x2=5,4x equation:

0.9x^2=5.4x

We move all terms to the left:

0.9x^2-(5.4x)=0

We add all the numbers together, and all the variables

0.9x^2-(+5.4x)=0

We get rid of parentheses

0.9x^2-5.4x=0

a = 0.9; b = -5.4; c = 0;
Δ = b2-4ac
Δ = -5.42-4·0.9·0
Δ = 29.16
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{-(-5.4)-\sqrt{29.16}}{2*0.9}=\frac{5.4-\sqrt{29.16}}{1.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.4)+\sqrt{29.16}}{2*0.9}=\frac{5.4+\sqrt{29.16}}{1.8}
$