3x^2=27x-9.5

Solution for 3x^2=27x-9.5 equation:

3x^2=27x-9.5

We move all terms to the left:

3x^2-(27x-9.5)=0

We get rid of parentheses

3x^2-27x+9.5=0

a = 3; b = -27; c = +9.5;
Δ = b2-4ac
Δ = -272-4·3·9.5
Δ = 615
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{-(-27)-\sqrt{615}}{2*3}=\frac{27-\sqrt{615}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{615}}{2*3}=\frac{27+\sqrt{615}}{6}
$