1/5x+2(3-1x)=-3

Solution for 1/5x+2(3-1x)=-3 equation:

1/5x+2(3-1x)=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

1/5x-2x+6+3=0

We multiply all the terms by the denominator


-2x*5x+6*5x+3*5x+1=0

Wy multiply elements

-10x^2+30x+15x+1=0

We add all the numbers together, and all the variables

-10x^2+45x+1=0

a = -10; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-10)·1
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2065}}{2*-10}=\frac{-45-\sqrt{2065}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2065}}{2*-10}=\frac{-45+\sqrt{2065}}{-20}
$