6x2-53x=9

Solution for 6x2-53x=9 equation:

6x^2-53x=9

We move all terms to the left:

6x^2-53x-(9)=0

a = 6; b = -53; c = -9;
Δ = b2-4ac
Δ = -532-4·6·(-9)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-55}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+55}{2*6}=\frac{108}{12}
=9
$