5a(a+80)+(2a+200)=360

Solution for 5a(a+80)+(2a+200)=360 equation:

5a(a+80)+(2a+200)=360

We move all terms to the left:

5a(a+80)+(2a+200)-(360)=0

We multiply parentheses

5a^2+400a+(2a+200)-360=0

We get rid of parentheses

5a^2+400a+2a+200-360=0

We add all the numbers together, and all the variables

5a^2+402a-160=0

a = 5; b = 402; c = -160;
Δ = b2-4ac
Δ = 4022-4·5·(-160)
Δ = 164804
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:

$\sqrt{\Delta}=\sqrt{164804}=\sqrt{4*41201}=\sqrt{4}*\sqrt{41201}=2\sqrt{41201}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(402)-2\sqrt{41201}}{2*5}=\frac{-402-2\sqrt{41201}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(402)+2\sqrt{41201}}{2*5}=\frac{-402+2\sqrt{41201}}{10}
$