4(x-1)=x+5x(x+10)

Solution for 4(x-1)=x+5x(x+10) equation:

4(x-1)=x+5x(x+10)

We move all terms to the left:

4(x-1)-(x+5x(x+10))=0

We multiply parentheses

4x-(x+5x(x+10))-4=0


We calculate terms in parentheses: -(x+5x(x+10)), so:

x+5x(x+10)

We multiply parentheses

5x^2+x+50x

We add all the numbers together, and all the variables

5x^2+51x

Back to the equation:

-(5x^2+51x)


We get rid of parentheses

-5x^2+4x-51x-4=0

We add all the numbers together, and all the variables

-5x^2-47x-4=0

a = -5; b = -47; c = -4;
Δ = b2-4ac
Δ = -472-4·(-5)·(-4)
Δ = 2129
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{-(-47)-\sqrt{2129}}{2*-5}=\frac{47-\sqrt{2129}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2129}}{2*-5}=\frac{47+\sqrt{2129}}{-10}
$