4/(5x-2)=14+42x

Solution for 4/(5x-2)=14+42x equation:

4/(5x-2)=14+42x

We move all terms to the left:

4/(5x-2)-(14+42x)=0


Domain of the equation: (5x-2)!=0

We move all terms containing x to the left, all other terms to the right

5x!=2

x!=2/5

x!=2/5

x∈R


We add all the numbers together, and all the variables

4/(5x-2)-(42x+14)=0

We get rid of parentheses

4/(5x-2)-42x-14=0

We multiply all the terms by the denominator


-42x*(5x-2)-14*(5x-2)+4=0

We multiply parentheses

-210x^2+84x-70x+28+4=0

We add all the numbers together, and all the variables

-210x^2+14x+32=0

a = -210; b = 14; c = +32;
Δ = b2-4ac
Δ = 142-4·(-210)·32
Δ = 27076
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:

$\sqrt{\Delta}=\sqrt{27076}=\sqrt{4*6769}=\sqrt{4}*\sqrt{6769}=2\sqrt{6769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{6769}}{2*-210}=\frac{-14-2\sqrt{6769}}{-420}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{6769}}{2*-210}=\frac{-14+2\sqrt{6769}}{-420}
$