x=(25-x)(x-7)

Solution for x=(25-x)(x-7) equation:

x=(25-x)(x-7)

We move all terms to the left:

x-((25-x)(x-7))=0

We add all the numbers together, and all the variables

x-((-1x+25)(x-7))=0

We multiply parentheses ..

-((-1x^2+7x+25x-175))+x=0


We calculate terms in parentheses: -((-1x^2+7x+25x-175)), so:

(-1x^2+7x+25x-175)

We get rid of parentheses

-1x^2+7x+25x-175

We add all the numbers together, and all the variables

-1x^2+32x-175

Back to the equation:

-(-1x^2+32x-175)


We get rid of parentheses

1x^2-32x+x+175=0

We add all the numbers together, and all the variables

x^2-31x+175=0

a = 1; b = -31; c = +175;
Δ = b2-4ac
Δ = -312-4·1·175
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-3\sqrt{29}}{2*1}=\frac{31-3\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+3\sqrt{29}}{2*1}=\frac{31+3\sqrt{29}}{2}
$