7x^2+28x-22=0

Solution for 7x^2+28x-22=0 equation:

7x^2+28x-22=0

a = 7; b = 28; c = -22;
Δ = b2-4ac
Δ = 282-4·7·(-22)
Δ = 1400
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:

$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-10\sqrt{14}}{2*7}=\frac{-28-10\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+10\sqrt{14}}{2*7}=\frac{-28+10\sqrt{14}}{14}
$