6x^2-13x=63

Solution for 6x^2-13x=63 equation:

6x^2-13x=63

We move all terms to the left:

6x^2-13x-(63)=0

a = 6; b = -13; c = -63;
Δ = b2-4ac
Δ = -132-4·6·(-63)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-41}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+41}{2*6}=\frac{54}{12}
=4+1/2
$