((a+3)*a)=17.5

Solution for ((a+3)*a)=17.5 equation:

((a+3)*a)=17.5

We move all terms to the left:

((a+3)*a)-(17.5)=0

We add all the numbers together, and all the variables

((a+3)*a)-17.5=0


We calculate terms in parentheses: +((a+3)*a), so:

(a+3)*a

We multiply parentheses

a^2+3a

Back to the equation:

+(a^2+3a)


We get rid of parentheses

a^2+3a-17.5=0

a = 1; b = 3; c = -17.5;
Δ = b2-4ac
Δ = 32-4·1·(-17.5)
Δ = 79
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{79}}{2*1}=\frac{-3-\sqrt{79}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{79}}{2*1}=\frac{-3+\sqrt{79}}{2}
$