-8/9x+32=10x-3

Solution for -8/9x+32=10x-3 equation:

-8/9x+32=10x-3

We move all terms to the left:

-8/9x+32-(10x-3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

-8/9x-10x+3+32=0

We multiply all the terms by the denominator


-10x*9x+3*9x+32*9x-8=0

Wy multiply elements

-90x^2+27x+288x-8=0

We add all the numbers together, and all the variables

-90x^2+315x-8=0

a = -90; b = 315; c = -8;
Δ = b2-4ac
Δ = 3152-4·(-90)·(-8)
Δ = 96345
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:

$\sqrt{\Delta}=\sqrt{96345}=\sqrt{9*10705}=\sqrt{9}*\sqrt{10705}=3\sqrt{10705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-3\sqrt{10705}}{2*-90}=\frac{-315-3\sqrt{10705}}{-180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+3\sqrt{10705}}{2*-90}=\frac{-315+3\sqrt{10705}}{-180}
$