90-x=(1/5)(180-x)-10

Solution for 90-x=(1/5)(180-x)-10 equation:

90-x=(1/5)(180-x)-10

We move all terms to the left:

90-x-((1/5)(180-x)-10)=0


Domain of the equation: 5)(180-x)-10)!=0

x∈R


We add all the numbers together, and all the variables

-x-((+1/5)(-1x+180)-10)+90=0

We add all the numbers together, and all the variables

-1x-((+1/5)(-1x+180)-10)+90=0

We multiply parentheses ..

-((-1x^2+1/5*180)-10)-1x+90=0

We multiply all the terms by the denominator


-((-1x^2+1-1x*5*180)-10)+90*5*180)-10)=0


We calculate terms in parentheses: -((-1x^2+1-1x*5*180)-10), so:

(-1x^2+1-1x*5*180)-10

We get rid of parentheses

-1x^2-1x*5*180+1-10

We add all the numbers together, and all the variables

-1x^2-1x*5*180-9

Wy multiply elements

-1x^2-900x*1-9

Wy multiply elements

-1x^2-900x-9

Back to the equation:

-(-1x^2-900x-9)


We add all the numbers together, and all the variables

-(-1x^2-900x-9)=0

We get rid of parentheses

1x^2+900x+9=0

We add all the numbers together, and all the variables

x^2+900x+9=0

a = 1; b = 900; c = +9;
Δ = b2-4ac
Δ = 9002-4·1·9
Δ = 809964
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:

$\sqrt{\Delta}=\sqrt{809964}=\sqrt{36*22499}=\sqrt{36}*\sqrt{22499}=6\sqrt{22499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-6\sqrt{22499}}{2*1}=\frac{-900-6\sqrt{22499}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+6\sqrt{22499}}{2*1}=\frac{-900+6\sqrt{22499}}{2}
$