(-15x-30/9x+84)=-1

Solution for (-15x-30/9x+84)=-1 equation:

(-15x-30/9x+84)=-1

We move all terms to the left:

(-15x-30/9x+84)-(-1)=0


Domain of the equation: 9x+84)!=0

x∈R


We add all the numbers together, and all the variables

(-15x-30/9x+84)+1=0

We get rid of parentheses

-15x-30/9x+84+1=0

We multiply all the terms by the denominator


-15x*9x+84*9x+1*9x-30=0

Wy multiply elements

-135x^2+756x+9x-30=0

We add all the numbers together, and all the variables

-135x^2+765x-30=0

a = -135; b = 765; c = -30;
Δ = b2-4ac
Δ = 7652-4·(-135)·(-30)
Δ = 569025
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:

$\sqrt{\Delta}=\sqrt{569025}=\sqrt{2025*281}=\sqrt{2025}*\sqrt{281}=45\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(765)-45\sqrt{281}}{2*-135}=\frac{-765-45\sqrt{281}}{-270}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(765)+45\sqrt{281}}{2*-135}=\frac{-765+45\sqrt{281}}{-270}
$