10r^2+7=647

Solution for 10r^2+7=647 equation:

10r^2+7=647

We move all terms to the left:

10r^2+7-(647)=0

We add all the numbers together, and all the variables

10r^2-640=0

a = 10; b = 0; c = -640;
Δ = b2-4ac
Δ = 02-4·10·(-640)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160}{2*10}=\frac{-160}{20}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160}{2*10}=\frac{160}{20}
=8
$