5a(8-a)=3a-20

Solution for 5a(8-a)=3a-20 equation:

5a(8-a)=3a-20

We move all terms to the left:

5a(8-a)-(3a-20)=0

We add all the numbers together, and all the variables

5a(-1a+8)-(3a-20)=0

We multiply parentheses

-5a^2+40a-(3a-20)=0

We get rid of parentheses

-5a^2+40a-3a+20=0

We add all the numbers together, and all the variables

-5a^2+37a+20=0

a = -5; b = 37; c = +20;
Δ = b2-4ac
Δ = 372-4·(-5)·20
Δ = 1769
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{-(37)-\sqrt{1769}}{2*-5}=\frac{-37-\sqrt{1769}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1769}}{2*-5}=\frac{-37+\sqrt{1769}}{-10}
$