7x-13/6x=1

Solution for 7x-13/6x=1 equation:

7x-13/6x=1

We move all terms to the left:

7x-13/6x-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


7x*6x-1*6x-13=0

Wy multiply elements

42x^2-6x-13=0

a = 42; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·42·(-13)
Δ = 2220
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:

$\sqrt{\Delta}=\sqrt{2220}=\sqrt{4*555}=\sqrt{4}*\sqrt{555}=2\sqrt{555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{555}}{2*42}=\frac{6-2\sqrt{555}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{555}}{2*42}=\frac{6+2\sqrt{555}}{84}
$