9x-6/5x+12=10

Solution for 9x-6/5x+12=10 equation:

9x-6/5x+12=10

We move all terms to the left:

9x-6/5x+12-(10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

9x-6/5x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

45x^2+10x-6=0

a = 45; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·45·(-6)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{295}}{2*45}=\frac{-10-2\sqrt{295}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{295}}{2*45}=\frac{-10+2\sqrt{295}}{90}
$