440=x(4x+5)

Solution for 440=x(4x+5) equation:

440=x(4x+5)

We move all terms to the left:

440-(x(4x+5))=0


We calculate terms in parentheses: -(x(4x+5)), so:

x(4x+5)

We multiply parentheses

4x^2+5x

Back to the equation:

-(4x^2+5x)


We get rid of parentheses

-4x^2-5x+440=0

a = -4; b = -5; c = +440;
Δ = b2-4ac
Δ = -52-4·(-4)·440
Δ = 7065
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:

$\sqrt{\Delta}=\sqrt{7065}=\sqrt{9*785}=\sqrt{9}*\sqrt{785}=3\sqrt{785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{785}}{2*-4}=\frac{5-3\sqrt{785}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{785}}{2*-4}=\frac{5+3\sqrt{785}}{-8}
$