3x^2-45x=6

Solution for 3x^2-45x=6 equation:

3x^2-45x=6

We move all terms to the left:

3x^2-45x-(6)=0

a = 3; b = -45; c = -6;
Δ = b2-4ac
Δ = -452-4·3·(-6)
Δ = 2097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{233}}{2*3}=\frac{45-3\sqrt{233}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{233}}{2*3}=\frac{45+3\sqrt{233}}{6}
$