7x^2+28x-21=0

Solution for 7x^2+28x-21=0 equation:

7x^2+28x-21=0

a = 7; b = 28; c = -21;
Δ = b2-4ac
Δ = 282-4·7·(-21)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-14\sqrt{7}}{2*7}=\frac{-28-14\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14\sqrt{7}}{2*7}=\frac{-28+14\sqrt{7}}{14}
$