r^2-74+4r=3

Solution for r^2-74+4r=3 equation:

r^2-74+4r=3

We move all terms to the left:

r^2-74+4r-(3)=0

We add all the numbers together, and all the variables

r^2+4r-77=0

a = 1; b = 4; c = -77;
Δ = b2-4ac
Δ = 42-4·1·(-77)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-18}{2*1}=\frac{-22}{2}
=-11
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+18}{2*1}=\frac{14}{2}
=7
$