x=(10-x)(6-x)

Solution for x=(10-x)(6-x) equation:

x=(10-x)(6-x)

We move all terms to the left:

x-((10-x)(6-x))=0

We add all the numbers together, and all the variables

x-((-1x+10)(-1x+6))=0

We multiply parentheses ..

-((+x^2-6x-10x+60))+x=0


We calculate terms in parentheses: -((+x^2-6x-10x+60)), so:

(+x^2-6x-10x+60)

We get rid of parentheses

x^2-6x-10x+60

We add all the numbers together, and all the variables

x^2-16x+60

Back to the equation:

-(x^2-16x+60)


We add all the numbers together, and all the variables

x-(x^2-16x+60)=0

We get rid of parentheses

-x^2+x+16x-60=0

We add all the numbers together, and all the variables

-1x^2+17x-60=0

a = -1; b = 17; c = -60;
Δ = b2-4ac
Δ = 172-4·(-1)·(-60)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*-1}=\frac{-10}{-2}
=+5
$