3(x+5)14x=5(3x+1)-11x

Solution for 3(x+5)14x=5(3x+1)-11x equation:

3(x+5)14x=5(3x+1)-11x

We move all terms to the left:

3(x+5)14x-(5(3x+1)-11x)=0

We multiply parentheses

42x^2+210x-(5(3x+1)-11x)=0


We calculate terms in parentheses: -(5(3x+1)-11x), so:

5(3x+1)-11x

We add all the numbers together, and all the variables

-11x+5(3x+1)

We multiply parentheses

-11x+15x+5

We add all the numbers together, and all the variables

4x+5

Back to the equation:

-(4x+5)


We get rid of parentheses

42x^2+210x-4x-5=0

We add all the numbers together, and all the variables

42x^2+206x-5=0

a = 42; b = 206; c = -5;
Δ = b2-4ac
Δ = 2062-4·42·(-5)
Δ = 43276
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:

$\sqrt{\Delta}=\sqrt{43276}=\sqrt{4*10819}=\sqrt{4}*\sqrt{10819}=2\sqrt{10819}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-2\sqrt{10819}}{2*42}=\frac{-206-2\sqrt{10819}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+2\sqrt{10819}}{2*42}=\frac{-206+2\sqrt{10819}}{84}
$