6x^2-9x=405

Solution for 6x^2-9x=405 equation:

6x^2-9x=405

We move all terms to the left:

6x^2-9x-(405)=0

a = 6; b = -9; c = -405;
Δ = b2-4ac
Δ = -92-4·6·(-405)
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-99}{2*6}=\frac{-90}{12}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+99}{2*6}=\frac{108}{12}
=9
$