10r^2-29+10=0

Solution for 10r^2-29+10=0 equation:

10r^2-29+10=0

We add all the numbers together, and all the variables

10r^2-19=0

a = 10; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·10·(-19)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*10}=\frac{0-2\sqrt{190}}{20}
=-\frac{2\sqrt{190}}{20}
=-\frac{\sqrt{190}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*10}=\frac{0+2\sqrt{190}}{20}
=\frac{2\sqrt{190}}{20}
=\frac{\sqrt{190}}{10}
$