30a^2+17a-21=0

Solution for 30a^2+17a-21=0 equation:

30a^2+17a-21=0

a = 30; b = 17; c = -21;
Δ = b2-4ac
Δ = 172-4·30·(-21)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-53}{2*30}=\frac{-70}{60}
=-1+1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+53}{2*30}=\frac{36}{60}
=3/5
$