2(5m+3)8m=4

Solution for 2(5m+3)8m=4 equation:

2(5m+3)8m=4

We move all terms to the left:

2(5m+3)8m-(4)=0

We multiply parentheses

80m^2+48m-4=0

a = 80; b = 48; c = -4;
Δ = b2-4ac
Δ = 482-4·80·(-4)
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{14}}{2*80}=\frac{-48-16\sqrt{14}}{160}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{14}}{2*80}=\frac{-48+16\sqrt{14}}{160}
$