2/9x+5=7x-90

Solution for 2/9x+5=7x-90 equation:

2/9x+5=7x-90

We move all terms to the left:

2/9x+5-(7x-90)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

2/9x-7x+90+5=0

We multiply all the terms by the denominator


-7x*9x+90*9x+5*9x+2=0

Wy multiply elements

-63x^2+810x+45x+2=0

We add all the numbers together, and all the variables

-63x^2+855x+2=0

a = -63; b = 855; c = +2;
Δ = b2-4ac
Δ = 8552-4·(-63)·2
Δ = 731529
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:

$\sqrt{\Delta}=\sqrt{731529}=\sqrt{9*81281}=\sqrt{9}*\sqrt{81281}=3\sqrt{81281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(855)-3\sqrt{81281}}{2*-63}=\frac{-855-3\sqrt{81281}}{-126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(855)+3\sqrt{81281}}{2*-63}=\frac{-855+3\sqrt{81281}}{-126}
$