9x-10/12x=0

Solution for 9x-10/12x=0 equation:

9x-10/12x=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We multiply all the terms by the denominator


9x*12x-10=0

Wy multiply elements

108x^2-10=0

a = 108; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·108·(-10)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*108}=\frac{0-12\sqrt{30}}{216}
=-\frac{12\sqrt{30}}{216}
=-\frac{\sqrt{30}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*108}=\frac{0+12\sqrt{30}}{216}
=\frac{12\sqrt{30}}{216}
=\frac{\sqrt{30}}{18}
$