2r^2-4r-3=5

Solution for 2r^2-4r-3=5 equation:

2r^2-4r-3=5

We move all terms to the left:

2r^2-4r-3-(5)=0

We add all the numbers together, and all the variables

2r^2-4r-8=0

a = 2; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·2·(-8)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*2}=\frac{4-4\sqrt{5}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*2}=\frac{4+4\sqrt{5}}{4}
$