6x^2-x-57=0

Solution for 6x^2-x-57=0 equation:

6x^2-x-57=0

We add all the numbers together, and all the variables

6x^2-1x-57=0

a = 6; b = -1; c = -57;
Δ = b2-4ac
Δ = -12-4·6·(-57)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-37}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+37}{2*6}=\frac{38}{12}
=3+1/6
$