9a*2+a2=90

Solution for 9a*2+a2=90 equation:

9a*2+a2=90

We move all terms to the left:

9a*2+a2-(90)=0

We add all the numbers together, and all the variables

a^2+9a*2-90=0

Wy multiply elements

a^2+18a-90=0

a = 1; b = 18; c = -90;
Δ = b2-4ac
Δ = 182-4·1·(-90)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{19}}{2*1}=\frac{-18-6\sqrt{19}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{19}}{2*1}=\frac{-18+6\sqrt{19}}{2}
$