(m+314)(4m+8)=180

Solution for (m+314)(4m+8)=180 equation:

(m+314)(4m+8)=180

We move all terms to the left:

(m+314)(4m+8)-(180)=0

We multiply parentheses ..

(+4m^2+8m+1256m+2512)-180=0

We get rid of parentheses

4m^2+8m+1256m+2512-180=0

We add all the numbers together, and all the variables

4m^2+1264m+2332=0

a = 4; b = 1264; c = +2332;
Δ = b2-4ac
Δ = 12642-4·4·2332
Δ = 1560384
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:

$\sqrt{\Delta}=\sqrt{1560384}=\sqrt{5184*301}=\sqrt{5184}*\sqrt{301}=72\sqrt{301}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1264)-72\sqrt{301}}{2*4}=\frac{-1264-72\sqrt{301}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1264)+72\sqrt{301}}{2*4}=\frac{-1264+72\sqrt{301}}{8}
$