3x^2-9x=5

Solution for 3x^2-9x=5 equation:

3x^2-9x=5

We move all terms to the left:

3x^2-9x-(5)=0

a = 3; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·3·(-5)
Δ = 141
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{-(-9)-\sqrt{141}}{2*3}=\frac{9-\sqrt{141}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{141}}{2*3}=\frac{9+\sqrt{141}}{6}
$