/10x+9=4x-9*

Solution for /10x+9=4x-9* equation:

/10x+9=4x-9*

We move all terms to the left:

/10x+9-(4x-9*)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

/10x-(+4x)+9=0

We get rid of parentheses

/10x-4x+9=0

We multiply all the terms by the denominator


-4x*10x+9*10x+=0

We add all the numbers together, and all the variables

-4x*10x+9*10x=0

Wy multiply elements

-40x^2+90x=0

a = -40; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-40)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-40}=\frac{-180}{-80}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-40}=\frac{0}{-80}
=0
$