3x(x-2)-(1-x)=13

Solution for 3x(x-2)-(1-x)=13 equation:

3x(x-2)-(1-x)=13

We move all terms to the left:

3x(x-2)-(1-x)-(13)=0

We add all the numbers together, and all the variables

3x(x-2)-(-1x+1)-13=0

We multiply parentheses

3x^2-6x-(-1x+1)-13=0

We get rid of parentheses

3x^2-6x+1x-1-13=0

We add all the numbers together, and all the variables

3x^2-5x-14=0

a = 3; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·3·(-14)
Δ = 193
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{-(-5)-\sqrt{193}}{2*3}=\frac{5-\sqrt{193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*3}=\frac{5+\sqrt{193}}{6}
$