4r^2-8r-14=0

Solution for 4r^2-8r-14=0 equation:

4r^2-8r-14=0

a = 4; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·4·(-14)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{2}}{2*4}=\frac{8-12\sqrt{2}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*4}=\frac{8+12\sqrt{2}}{8}
$