5/2x+6=5x-9

Solution for 5/2x+6=5x-9 equation:

5/2x+6=5x-9

We move all terms to the left:

5/2x+6-(5x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-5x+9+6=0

We multiply all the terms by the denominator


-5x*2x+9*2x+6*2x+5=0

Wy multiply elements

-10x^2+18x+12x+5=0

We add all the numbers together, and all the variables

-10x^2+30x+5=0

a = -10; b = 30; c = +5;
Δ = b2-4ac
Δ = 302-4·(-10)·5
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{11}}{2*-10}=\frac{-30-10\sqrt{11}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{11}}{2*-10}=\frac{-30+10\sqrt{11}}{-20}
$