2a(3-a)=5a-8

Solution for 2a(3-a)=5a-8 equation:

2a(3-a)=5a-8

We move all terms to the left:

2a(3-a)-(5a-8)=0

We add all the numbers together, and all the variables

2a(-1a+3)-(5a-8)=0

We multiply parentheses

-2a^2+6a-(5a-8)=0

We get rid of parentheses

-2a^2+6a-5a+8=0

We add all the numbers together, and all the variables

-2a^2+a+8=0

a = -2; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-2)·8
Δ = 65
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{-(1)-\sqrt{65}}{2*-2}=\frac{-1-\sqrt{65}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*-2}=\frac{-1+\sqrt{65}}{-4}
$