2x-15/6x=7

Solution for 2x-15/6x=7 equation:

2x-15/6x=7

We move all terms to the left:

2x-15/6x-(7)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


2x*6x-7*6x-15=0

Wy multiply elements

12x^2-42x-15=0

a = 12; b = -42; c = -15;
Δ = b2-4ac
Δ = -422-4·12·(-15)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{69}}{2*12}=\frac{42-6\sqrt{69}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{69}}{2*12}=\frac{42+6\sqrt{69}}{24}
$