21z^2+46z+7=0

Solution for 21z^2+46z+7=0 equation:

21z^2+46z+7=0

a = 21; b = 46; c = +7;
Δ = b2-4ac
Δ = 462-4·21·7
Δ = 1528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1528}=\sqrt{4*382}=\sqrt{4}*\sqrt{382}=2\sqrt{382}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{382}}{2*21}=\frac{-46-2\sqrt{382}}{42}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{382}}{2*21}=\frac{-46+2\sqrt{382}}{42}
$