44+2a(a+10)=180

Solution for 44+2a(a+10)=180 equation:

44+2a(a+10)=180

We move all terms to the left:

44+2a(a+10)-(180)=0

We add all the numbers together, and all the variables

2a(a+10)-136=0

We multiply parentheses

2a^2+20a-136=0

a = 2; b = 20; c = -136;
Δ = b2-4ac
Δ = 202-4·2·(-136)
Δ = 1488
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{93}}{2*2}=\frac{-20-4\sqrt{93}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{93}}{2*2}=\frac{-20+4\sqrt{93}}{4}
$