3x+4=5x(x-8)

Solution for 3x+4=5x(x-8) equation:

3x+4=5x(x-8)

We move all terms to the left:

3x+4-(5x(x-8))=0


We calculate terms in parentheses: -(5x(x-8)), so:

5x(x-8)

We multiply parentheses

5x^2-40x

Back to the equation:

-(5x^2-40x)


We get rid of parentheses

-5x^2+3x+40x+4=0

We add all the numbers together, and all the variables

-5x^2+43x+4=0

a = -5; b = 43; c = +4;
Δ = b2-4ac
Δ = 432-4·(-5)·4
Δ = 1929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{1929}}{2*-5}=\frac{-43-\sqrt{1929}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{1929}}{2*-5}=\frac{-43+\sqrt{1929}}{-10}
$