2a(a+10)+44=90

Solution for 2a(a+10)+44=90 equation:

2a(a+10)+44=90

We move all terms to the left:

2a(a+10)+44-(90)=0

We add all the numbers together, and all the variables

2a(a+10)-46=0

We multiply parentheses

2a^2+20a-46=0

a = 2; b = 20; c = -46;
Δ = b2-4ac
Δ = 202-4·2·(-46)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-16\sqrt{3}}{2*2}=\frac{-20-16\sqrt{3}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+16\sqrt{3}}{2*2}=\frac{-20+16\sqrt{3}}{4}
$