7r^2-42=7r

Solution for 7r^2-42=7r equation:

7r^2-42=7r

We move all terms to the left:

7r^2-42-(7r)=0

a = 7; b = -7; c = -42;
Δ = b2-4ac
Δ = -72-4·7·(-42)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-35}{2*7}=\frac{-28}{14}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+35}{2*7}=\frac{42}{14}
=3
$