4+x=8x(x-3)

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

4+x=8x(x-3)

We move all terms to the left:

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


We calculate terms in parentheses: -(8x(x-3)), so:

8x(x-3)

We multiply parentheses

8x^2-24x

Back to the equation:

-(8x^2-24x)


We get rid of parentheses

-8x^2+x+24x+4=0

We add all the numbers together, and all the variables

-8x^2+25x+4=0

a = -8; b = 25; c = +4;
Δ = b2-4ac
Δ = 252-4·(-8)·4
Δ = 753
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{-(25)-\sqrt{753}}{2*-8}=\frac{-25-\sqrt{753}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{753}}{2*-8}=\frac{-25+\sqrt{753}}{-16}
$