6a^2-23a+7=0

Solution for 6a^2-23a+7=0 equation:

6a^2-23a+7=0

a = 6; b = -23; c = +7;
Δ = b2-4ac
Δ = -232-4·6·7
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*6}=\frac{4}{12}
=1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*6}=\frac{42}{12}
=3+1/2
$