15x-1=11/2x+2

Solution for 15x-1=11/2x+2 equation:

15x-1=11/2x+2

We move all terms to the left:

15x-1-(11/2x+2)=0


Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

15x-11/2x-2-1=0

We multiply all the terms by the denominator


15x*2x-2*2x-1*2x-11=0

Wy multiply elements

30x^2-4x-2x-11=0

We add all the numbers together, and all the variables

30x^2-6x-11=0

a = 30; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·30·(-11)
Δ = 1356
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:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{339}}{2*30}=\frac{6-2\sqrt{339}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{339}}{2*30}=\frac{6+2\sqrt{339}}{60}
$