1/5x-9=7.5+6x

Solution for 1/5x-9=7.5+6x equation:

1/5x-9=7.5+6x

We move all terms to the left:

1/5x-9-(7.5+6x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(6x+7.5)-9=0

We get rid of parentheses

1/5x-6x-7.5-9=0

We multiply all the terms by the denominator


-6x*5x-(7.5)*5x-9*5x+1=0

We multiply parentheses

-6x*5x-37.5x-9*5x+1=0

Wy multiply elements

-30x^2-37.5x-45x+1=0

We add all the numbers together, and all the variables

-30x^2-82.5x+1=0

a = -30; b = -82.5; c = +1;
Δ = b2-4ac
Δ = -82.52-4·(-30)·1
Δ = 6926.25
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{-(-82.5)-\sqrt{6926.25}}{2*-30}=\frac{82.5-\sqrt{6926.25}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82.5)+\sqrt{6926.25}}{2*-30}=\frac{82.5+\sqrt{6926.25}}{-60}
$