412=0.54x^2+1.1x

Solution for 412=0.54x^2+1.1x equation:

412=0.54x^2+1.1x

We move all terms to the left:

412-(0.54x^2+1.1x)=0

We get rid of parentheses

-0.54x^2-1.1x+412=0

a = -0.54; b = -1.1; c = +412;
Δ = b2-4ac
Δ = -1.12-4·(-0.54)·412
Δ = 891.13
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{-(-1.1)-\sqrt{891.13}}{2*-0.54}=\frac{1.1-\sqrt{891.13}}{-1.08}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.1)+\sqrt{891.13}}{2*-0.54}=\frac{1.1+\sqrt{891.13}}{-1.08}
$