21-2x=(5x+4)(x-1)

Solution for 21-2x=(5x+4)(x-1) equation:

21-2x=(5x+4)(x-1)

We move all terms to the left:

21-2x-((5x+4)(x-1))=0

We multiply parentheses ..

-((+5x^2-5x+4x-4))-2x+21=0


We calculate terms in parentheses: -((+5x^2-5x+4x-4)), so:

(+5x^2-5x+4x-4)

We get rid of parentheses

5x^2-5x+4x-4

We add all the numbers together, and all the variables

5x^2-1x-4

Back to the equation:

-(5x^2-1x-4)


We add all the numbers together, and all the variables

-2x-(5x^2-1x-4)+21=0

We get rid of parentheses

-5x^2-2x+1x+4+21=0

We add all the numbers together, and all the variables

-5x^2-1x+25=0

a = -5; b = -1; c = +25;
Δ = b2-4ac
Δ = -12-4·(-5)·25
Δ = 501
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{-(-1)-\sqrt{501}}{2*-5}=\frac{1-\sqrt{501}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{501}}{2*-5}=\frac{1+\sqrt{501}}{-10}
$