2r^2=7r-2

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

2r^2=7r-2

We move all terms to the left:

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

We get rid of parentheses

2r^2-7r+2=0

a = 2; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·2·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{33}}{2*2}=\frac{7-\sqrt{33}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*2}=\frac{7+\sqrt{33}}{4}
$