1/5x-2+2/5x=7+15x-3

Solution for 1/5x-2+2/5x=7+15x-3 equation:

1/5x-2+2/5x=7+15x-3

We move all terms to the left:

1/5x-2+2/5x-(7+15x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+2/5x-(15x+4)-2=0

We get rid of parentheses

1/5x+2/5x-15x-4-2=0

We multiply all the terms by the denominator


-15x*5x-4*5x-2*5x+1+2=0

We add all the numbers together, and all the variables

-15x*5x-4*5x-2*5x+3=0

Wy multiply elements

-75x^2-20x-10x+3=0

We add all the numbers together, and all the variables

-75x^2-30x+3=0

a = -75; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-75)·3
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{2}}{2*-75}=\frac{30-30\sqrt{2}}{-150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{2}}{2*-75}=\frac{30+30\sqrt{2}}{-150}
$