-1/5x+90=-2x+9

Solution for -1/5x+90=-2x+9 equation:

-1/5x+90=-2x+9

We move all terms to the left:

-1/5x+90-(-2x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x+2x-9+90=0

We multiply all the terms by the denominator


2x*5x-9*5x+90*5x-1=0

Wy multiply elements

10x^2-45x+450x-1=0

We add all the numbers together, and all the variables

10x^2+405x-1=0

a = 10; b = 405; c = -1;
Δ = b2-4ac
Δ = 4052-4·10·(-1)
Δ = 164065
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{-(405)-\sqrt{164065}}{2*10}=\frac{-405-\sqrt{164065}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(405)+\sqrt{164065}}{2*10}=\frac{-405+\sqrt{164065}}{20}
$