-2.7x^2+30x=5.5

Solution for -2.7x^2+30x=5.5 equation:

-2.7x^2+30x=5.5

We move all terms to the left:

-2.7x^2+30x-(5.5)=0

We add all the numbers together, and all the variables

-2.7x^2+30x-5.5=0

a = -2.7; b = 30; c = -5.5;
Δ = b2-4ac
Δ = 302-4·(-2.7)·(-5.5)
Δ = 840.6
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{-(30)-\sqrt{840.6}}{2*-2.7}=\frac{-30-\sqrt{840.6}}{-5.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{840.6}}{2*-2.7}=\frac{-30+\sqrt{840.6}}{-5.4}
$