6a^2-43a+42=0

Solution for 6a^2-43a+42=0 equation:

6a^2-43a+42=0

a = 6; b = -43; c = +42;
Δ = b2-4ac
Δ = -432-4·6·42
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-29}{2*6}=\frac{14}{12}
=1+1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+29}{2*6}=\frac{72}{12}
=6
$