1440=(4x-1)(x+5)

Solution for 1440=(4x-1)(x+5) equation:

1440=(4x-1)(x+5)

We move all terms to the left:

1440-((4x-1)(x+5))=0

We multiply parentheses ..

-((+4x^2+20x-1x-5))+1440=0


We calculate terms in parentheses: -((+4x^2+20x-1x-5)), so:

(+4x^2+20x-1x-5)

We get rid of parentheses

4x^2+20x-1x-5

We add all the numbers together, and all the variables

4x^2+19x-5

Back to the equation:

-(4x^2+19x-5)


We get rid of parentheses

-4x^2-19x+5+1440=0

We add all the numbers together, and all the variables

-4x^2-19x+1445=0

a = -4; b = -19; c = +1445;
Δ = b2-4ac
Δ = -192-4·(-4)·1445
Δ = 23481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23481}=\sqrt{9*2609}=\sqrt{9}*\sqrt{2609}=3\sqrt{2609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{2609}}{2*-4}=\frac{19-3\sqrt{2609}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{2609}}{2*-4}=\frac{19+3\sqrt{2609}}{-8}
$