10r^2=45-68r

Solution for 10r^2=45-68r equation:

10r^2=45-68r

We move all terms to the left:

10r^2-(45-68r)=0

We add all the numbers together, and all the variables

10r^2-(-68r+45)=0

We get rid of parentheses

10r^2+68r-45=0

a = 10; b = 68; c = -45;
Δ = b2-4ac
Δ = 682-4·10·(-45)
Δ = 6424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6424}=\sqrt{4*1606}=\sqrt{4}*\sqrt{1606}=2\sqrt{1606}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1606}}{2*10}=\frac{-68-2\sqrt{1606}}{20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1606}}{2*10}=\frac{-68+2\sqrt{1606}}{20}
$