2a^2+4a-21=0

Solution for 2a^2+4a-21=0 equation:

2a^2+4a-21=0

a = 2; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·2·(-21)
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*2}=\frac{-4-2\sqrt{46}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*2}=\frac{-4+2\sqrt{46}}{4}
$