4x-1/5x+7=5

Solution for 4x-1/5x+7=5 equation:

4x-1/5x+7=5

We move all terms to the left:

4x-1/5x+7-(5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4x-1/5x+2=0

We multiply all the terms by the denominator


4x*5x+2*5x-1=0

Wy multiply elements

20x^2+10x-1=0

a = 20; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·20·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*20}=\frac{-10-6\sqrt{5}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*20}=\frac{-10+6\sqrt{5}}{40}
$