4a+(a*a)=180

Solution for 4a+(a*a)=180 equation:

4a+(a*a)=180

We move all terms to the left:

4a+(a*a)-(180)=0

We add all the numbers together, and all the variables

4a+(+a*a)-180=0

We get rid of parentheses

4a+a*a-180=0

Wy multiply elements

a^2+4a-180=0

a = 1; b = 4; c = -180;
Δ = b2-4ac
Δ = 42-4·1·(-180)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{46}}{2*1}=\frac{-4-4\sqrt{46}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{46}}{2*1}=\frac{-4+4\sqrt{46}}{2}
$