7r^2=11r-4

Solution for 7r^2=11r-4 equation:

7r^2=11r-4

We move all terms to the left:

7r^2-(11r-4)=0

We get rid of parentheses

7r^2-11r+4=0

a = 7; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·7·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*7}=\frac{8}{14}
=4/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*7}=\frac{14}{14}
=1
$