3X2+4x-21=0

Solution for 3X2+4x-21=0 equation:

3X^2+4X-21=0

a = 3; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·3·(-21)
Δ = 268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{67}}{2*3}=\frac{-4-2\sqrt{67}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{67}}{2*3}=\frac{-4+2\sqrt{67}}{6}
$