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 = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{321}}{2*24}=\frac{42-2\sqrt{321}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{321}}{2*24}=\frac{42+2\sqrt{321}}{48}
$