10p^2-5=835

Solution for 10p^2-5=835 equation:

10p^2-5=835

We move all terms to the left:

10p^2-5-(835)=0

We add all the numbers together, and all the variables

10p^2-840=0

a = 10; b = 0; c = -840;
Δ = b2-4ac
Δ = 02-4·10·(-840)
Δ = 33600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{33600}=\sqrt{1600*21}=\sqrt{1600}*\sqrt{21}=40\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{21}}{2*10}=\frac{0-40\sqrt{21}}{20}
=-\frac{40\sqrt{21}}{20}
=-2\sqrt{21}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{21}}{2*10}=\frac{0+40\sqrt{21}}{20}
=\frac{40\sqrt{21}}{20}
=2\sqrt{21}
$