(3-2x)(25-2x)=494

Solution for (3-2x)(25-2x)=494 equation:

(3-2x)(25-2x)=494

We move all terms to the left:

(3-2x)(25-2x)-(494)=0

We add all the numbers together, and all the variables

(-2x+3)(-2x+25)-494=0

We multiply parentheses ..

(+4x^2-50x-6x+75)-494=0

We get rid of parentheses

4x^2-50x-6x+75-494=0

We add all the numbers together, and all the variables

4x^2-56x-419=0

a = 4; b = -56; c = -419;
Δ = b2-4ac
Δ = -562-4·4·(-419)
Δ = 9840
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:

$\sqrt{\Delta}=\sqrt{9840}=\sqrt{16*615}=\sqrt{16}*\sqrt{615}=4\sqrt{615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{615}}{2*4}=\frac{56-4\sqrt{615}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{615}}{2*4}=\frac{56+4\sqrt{615}}{8}
$