90-x=25-3x(180-x)

Solution for 90-x=25-3x(180-x) equation:

90-x=25-3x(180-x)

We move all terms to the left:

90-x-(25-3x(180-x))=0

We add all the numbers together, and all the variables

-x-(25-3x(-1x+180))+90=0

We add all the numbers together, and all the variables

-1x-(25-3x(-1x+180))+90=0


We calculate terms in parentheses: -(25-3x(-1x+180)), so:

25-3x(-1x+180)

determiningTheFunctionDomain
-3x(-1x+180)+25

We multiply parentheses

3x^2-540x+25

Back to the equation:

-(3x^2-540x+25)


We get rid of parentheses

-3x^2-1x+540x-25+90=0

We add all the numbers together, and all the variables

-3x^2+539x+65=0

a = -3; b = 539; c = +65;
Δ = b2-4ac
Δ = 5392-4·(-3)·65
Δ = 291301
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{-(539)-\sqrt{291301}}{2*-3}=\frac{-539-\sqrt{291301}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(539)+\sqrt{291301}}{2*-3}=\frac{-539+\sqrt{291301}}{-6}
$