4x(x-25)=25(1-4x)

Solution for 4x(x-25)=25(1-4x) equation:

4x(x-25)=25(1-4x)

We move all terms to the left:

4x(x-25)-(25(1-4x))=0

We add all the numbers together, and all the variables

4x(x-25)-(25(-4x+1))=0

We multiply parentheses

4x^2-100x-(25(-4x+1))=0


We calculate terms in parentheses: -(25(-4x+1)), so:

25(-4x+1)

We multiply parentheses

-100x+25

Back to the equation:

-(-100x+25)


We get rid of parentheses

4x^2-100x+100x-25=0

We add all the numbers together, and all the variables

4x^2-25=0

a = 4; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·4·(-25)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*4}=\frac{20}{8}
=2+1/2
$