3x+8/7x-6=0

Solution for 3x+8/7x-6=0 equation:

3x+8/7x-6=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


3x*7x-6*7x+8=0

Wy multiply elements

21x^2-42x+8=0

a = 21; b = -42; c = +8;
Δ = b2-4ac
Δ = -422-4·21·8
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{273}}{2*21}=\frac{42-2\sqrt{273}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{273}}{2*21}=\frac{42+2\sqrt{273}}{42}
$