4r^2=17-r

Solution for 4r^2=17-r equation:

4r^2=17-r

We move all terms to the left:

4r^2-(17-r)=0

We add all the numbers together, and all the variables

4r^2-(-1r+17)=0

We get rid of parentheses

4r^2+1r-17=0

We add all the numbers together, and all the variables

4r^2+r-17=0

a = 4; b = 1; c = -17;
Δ = b2-4ac
Δ = 12-4·4·(-17)
Δ = 273
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{-(1)-\sqrt{273}}{2*4}=\frac{-1-\sqrt{273}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{273}}{2*4}=\frac{-1+\sqrt{273}}{8}
$