5(1+4m)2m=59

Solution for 5(1+4m)2m=59 equation:

5(1+4m)2m=59

We move all terms to the left:

5(1+4m)2m-(59)=0

We add all the numbers together, and all the variables

5(4m+1)2m-59=0

We multiply parentheses

40m^2+10m-59=0

a = 40; b = 10; c = -59;
Δ = b2-4ac
Δ = 102-4·40·(-59)
Δ = 9540
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:

$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{265}}{2*40}=\frac{-10-6\sqrt{265}}{80}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{265}}{2*40}=\frac{-10+6\sqrt{265}}{80}
$