x-40/14x+28=0

Solution for x-40/14x+28=0 equation:

x-40/14x+28=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We multiply all the terms by the denominator


x*14x+28*14x-40=0

Wy multiply elements

14x^2+392x-40=0

a = 14; b = 392; c = -40;
Δ = b2-4ac
Δ = 3922-4·14·(-40)
Δ = 155904
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:

$\sqrt{\Delta}=\sqrt{155904}=\sqrt{256*609}=\sqrt{256}*\sqrt{609}=16\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(392)-16\sqrt{609}}{2*14}=\frac{-392-16\sqrt{609}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(392)+16\sqrt{609}}{2*14}=\frac{-392+16\sqrt{609}}{28}
$