2/5x+5x=6

Solution for 2/5x+5x=6 equation:

2/5x+5x=6

We move all terms to the left:

2/5x+5x-(6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5x+2/5x-6=0

We multiply all the terms by the denominator


5x*5x-6*5x+2=0

Wy multiply elements

25x^2-30x+2=0

a = 25; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·25·2
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{7}}{2*25}=\frac{30-10\sqrt{7}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{7}}{2*25}=\frac{30+10\sqrt{7}}{50}
$