2x+6/4x-140=0

Solution for 2x+6/4x-140=0 equation:

2x+6/4x-140=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-140*4x+6=0

Wy multiply elements

8x^2-560x+6=0

a = 8; b = -560; c = +6;
Δ = b2-4ac
Δ = -5602-4·8·6
Δ = 313408
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:

$\sqrt{\Delta}=\sqrt{313408}=\sqrt{64*4897}=\sqrt{64}*\sqrt{4897}=8\sqrt{4897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-560)-8\sqrt{4897}}{2*8}=\frac{560-8\sqrt{4897}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-560)+8\sqrt{4897}}{2*8}=\frac{560+8\sqrt{4897}}{16}
$