6p^2-29p-42=0

Solution for 6p^2-29p-42=0 equation:

6p^2-29p-42=0

a = 6; b = -29; c = -42;
Δ = b2-4ac
Δ = -292-4·6·(-42)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-43}{2*6}=\frac{-14}{12}
=-1+1/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+43}{2*6}=\frac{72}{12}
=6
$