10m^2=4m+45

Solution for 10m^2=4m+45 equation:

10m^2=4m+45

We move all terms to the left:

10m^2-(4m+45)=0

We get rid of parentheses

10m^2-4m-45=0

a = 10; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·10·(-45)
Δ = 1816
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:

$\sqrt{\Delta}=\sqrt{1816}=\sqrt{4*454}=\sqrt{4}*\sqrt{454}=2\sqrt{454}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{454}}{2*10}=\frac{4-2\sqrt{454}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{454}}{2*10}=\frac{4+2\sqrt{454}}{20}
$