10m^2-25m=45

Solution for 10m^2-25m=45 equation:

10m^2-25m=45

We move all terms to the left:

10m^2-25m-(45)=0

a = 10; b = -25; c = -45;
Δ = b2-4ac
Δ = -252-4·10·(-45)
Δ = 2425
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:

$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{97}}{2*10}=\frac{25-5\sqrt{97}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{97}}{2*10}=\frac{25+5\sqrt{97}}{20}
$