(x-10)(4x+20)=x

Solution for (x-10)(4x+20)=x equation:

(x-10)(4x+20)=x

We move all terms to the left:

(x-10)(4x+20)-(x)=0

We add all the numbers together, and all the variables

-1x+(x-10)(4x+20)=0

We multiply parentheses ..

(+4x^2+20x-40x-200)-1x=0

We get rid of parentheses

4x^2+20x-40x-1x-200=0

We add all the numbers together, and all the variables

4x^2-21x-200=0

a = 4; b = -21; c = -200;
Δ = b2-4ac
Δ = -212-4·4·(-200)
Δ = 3641
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{-(-21)-\sqrt{3641}}{2*4}=\frac{21-\sqrt{3641}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{3641}}{2*4}=\frac{21+\sqrt{3641}}{8}
$