7x^2+4x-22=0

Solution for 7x^2+4x-22=0 equation:

7x^2+4x-22=0

a = 7; b = 4; c = -22;
Δ = b2-4ac
Δ = 42-4·7·(-22)
Δ = 632
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:

$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{158}}{2*7}=\frac{-4-2\sqrt{158}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{158}}{2*7}=\frac{-4+2\sqrt{158}}{14}
$