3a+14=(5a-1)(4a-8)

Solution for 3a+14=(5a-1)(4a-8) equation:

3a+14=(5a-1)(4a-8)

We move all terms to the left:

3a+14-((5a-1)(4a-8))=0

We multiply parentheses ..

-((+20a^2-40a-4a+8))+3a+14=0


We calculate terms in parentheses: -((+20a^2-40a-4a+8)), so:

(+20a^2-40a-4a+8)

We get rid of parentheses

20a^2-40a-4a+8

We add all the numbers together, and all the variables

20a^2-44a+8

Back to the equation:

-(20a^2-44a+8)


We add all the numbers together, and all the variables

3a-(20a^2-44a+8)+14=0

We get rid of parentheses

-20a^2+3a+44a-8+14=0

We add all the numbers together, and all the variables

-20a^2+47a+6=0

a = -20; b = 47; c = +6;
Δ = b2-4ac
Δ = 472-4·(-20)·6
Δ = 2689
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{-(47)-\sqrt{2689}}{2*-20}=\frac{-47-\sqrt{2689}}{-40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{2689}}{2*-20}=\frac{-47+\sqrt{2689}}{-40}
$