2a2-14a-21=0

Solution for 2a2-14a-21=0 equation:

2a^2-14a-21=0

a = 2; b = -14; c = -21;
Δ = b2-4ac
Δ = -142-4·2·(-21)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{91}}{2*2}=\frac{14-2\sqrt{91}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{91}}{2*2}=\frac{14+2\sqrt{91}}{4}
$