36x-9/2x=15

Solution for 36x-9/2x=15 equation:

36x-9/2x=15

We move all terms to the left:

36x-9/2x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


36x*2x-15*2x-9=0

Wy multiply elements

72x^2-30x-9=0

a = 72; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·72·(-9)
Δ = 3492
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:

$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{97}}{2*72}=\frac{30-6\sqrt{97}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{97}}{2*72}=\frac{30+6\sqrt{97}}{144}
$