10m^2+7=827

Solution for 10m^2+7=827 equation:

10m^2+7=827

We move all terms to the left:

10m^2+7-(827)=0

We add all the numbers together, and all the variables

10m^2-820=0

a = 10; b = 0; c = -820;
Δ = b2-4ac
Δ = 02-4·10·(-820)
Δ = 32800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32800}=\sqrt{400*82}=\sqrt{400}*\sqrt{82}=20\sqrt{82}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{82}}{2*10}=\frac{0-20\sqrt{82}}{20}
=-\frac{20\sqrt{82}}{20}
=-\sqrt{82}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{82}}{2*10}=\frac{0+20\sqrt{82}}{20}
=\frac{20\sqrt{82}}{20}
=\sqrt{82}
$