(x+1)(x-5)=(4x)(-x+3)

Solution for (x+1)(x-5)=(4x)(-x+3) equation:

(x+1)(x-5)=(4x)(-x+3)

We move all terms to the left:

(x+1)(x-5)-((4x)(-x+3))=0

We add all the numbers together, and all the variables

(x+1)(x-5)-(4x(-1x+3))=0

We multiply parentheses ..

(+x^2-5x+x-5)-(4x(-1x+3))=0


We calculate terms in parentheses: -(4x(-1x+3)), so:

4x(-1x+3)

We multiply parentheses

-4x^2+12x

Back to the equation:

-(-4x^2+12x)


We get rid of parentheses

x^2+4x^2-5x+x-12x-5=0

We add all the numbers together, and all the variables

5x^2-16x-5=0

a = 5; b = -16; c = -5;
Δ = b2-4ac
Δ = -162-4·5·(-5)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{89}}{2*5}=\frac{16-2\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{89}}{2*5}=\frac{16+2\sqrt{89}}{10}
$