9x=5/2x-160

Solution for 9x=5/2x-160 equation:

9x=5/2x-160

We move all terms to the left:

9x-(5/2x-160)=0


Domain of the equation: 2x-160)!=0

x∈R


We get rid of parentheses

9x-5/2x+160=0

We multiply all the terms by the denominator


9x*2x+160*2x-5=0

Wy multiply elements

18x^2+320x-5=0

a = 18; b = 320; c = -5;
Δ = b2-4ac
Δ = 3202-4·18·(-5)
Δ = 102760
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:

$\sqrt{\Delta}=\sqrt{102760}=\sqrt{4*25690}=\sqrt{4}*\sqrt{25690}=2\sqrt{25690}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-2\sqrt{25690}}{2*18}=\frac{-320-2\sqrt{25690}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+2\sqrt{25690}}{2*18}=\frac{-320+2\sqrt{25690}}{36}
$