10x-12/5x-6=1

Solution for 10x-12/5x-6=1 equation:

10x-12/5x-6=1

We move all terms to the left:

10x-12/5x-6-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

10x-12/5x-7=0

We multiply all the terms by the denominator


10x*5x-7*5x-12=0

Wy multiply elements

50x^2-35x-12=0

a = 50; b = -35; c = -12;
Δ = b2-4ac
Δ = -352-4·50·(-12)
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{145}}{2*50}=\frac{35-5\sqrt{145}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{145}}{2*50}=\frac{35+5\sqrt{145}}{100}
$