10r^2-40=59r+2r^2

Solution for 10r^2-40=59r+2r^2 equation:

10r^2-40=59r+2r^2

We move all terms to the left:

10r^2-40-(59r+2r^2)=0

We get rid of parentheses

10r^2-2r^2-59r-40=0

We add all the numbers together, and all the variables

8r^2-59r-40=0

a = 8; b = -59; c = -40;
Δ = b2-4ac
Δ = -592-4·8·(-40)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-69}{2*8}=\frac{-10}{16}
=-5/8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+69}{2*8}=\frac{128}{16}
=8
$