7.4a(a+3)=3.2a+43.2

Solution for 7.4a(a+3)=3.2a+43.2 equation:

7.4a(a+3)=3.2a+43.2

We move all terms to the left:

7.4a(a+3)-(3.2a+43.2)=0

We multiply parentheses

7a^2+21a-(3.2a+43.2)=0

We get rid of parentheses

7a^2+21a-3.2a-43.2=0

We add all the numbers together, and all the variables

7a^2+17.8a-43.2=0

a = 7; b = 17.8; c = -43.2;
Δ = b2-4ac
Δ = 17.82-4·7·(-43.2)
Δ = 1526.44
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{-(17.8)-\sqrt{1526.44}}{2*7}=\frac{-17.8-\sqrt{1526.44}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17.8)+\sqrt{1526.44}}{2*7}=\frac{-17.8+\sqrt{1526.44}}{14}
$