5a(8-a)=4a-1.5

Solution for 5a(8-a)=4a-1.5 equation:

5a(8-a)=4a-1.5

We move all terms to the left:

5a(8-a)-(4a-1.5)=0

We add all the numbers together, and all the variables

5a(-1a+8)-(4a-1.5)=0

We multiply parentheses

-5a^2+40a-(4a-1.5)=0

We get rid of parentheses

-5a^2+40a-4a+1.5=0

We add all the numbers together, and all the variables

-5a^2+36a+1.5=0

a = -5; b = 36; c = +1.5;
Δ = b2-4ac
Δ = 362-4·(-5)·1.5
Δ = 1326
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{-(36)-\sqrt{1326}}{2*-5}=\frac{-36-\sqrt{1326}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+\sqrt{1326}}{2*-5}=\frac{-36+\sqrt{1326}}{-10}
$