4x-5/6x-7=0

Solution for 4x-5/6x-7=0 equation:

4x-5/6x-7=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


4x*6x-7*6x-5=0

Wy multiply elements

24x^2-42x-5=0

a = 24; b = -42; c = -5;
Δ = b2-4ac
Δ = -422-4·24·(-5)
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{561}}{2*24}=\frac{42-2\sqrt{561}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{561}}{2*24}=\frac{42+2\sqrt{561}}{48}
$