6x=9/2x+15

Solution for 6x=9/2x+15 equation:

6x=9/2x+15

We move all terms to the left:

6x-(9/2x+15)=0


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

6x-9/2x-15=0

We multiply all the terms by the denominator


6x*2x-15*2x-9=0

Wy multiply elements

12x^2-30x-9=0

a = 12; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·12·(-9)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{37}}{2*12}=\frac{30-6\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{37}}{2*12}=\frac{30+6\sqrt{37}}{24}
$