4x(x+3)-(1-x)=1

Solution for 4x(x+3)-(1-x)=1 equation:

4x(x+3)-(1-x)=1

We move all terms to the left:

4x(x+3)-(1-x)-(1)=0

We add all the numbers together, and all the variables

4x(x+3)-(-1x+1)-1=0

We multiply parentheses

4x^2+12x-(-1x+1)-1=0

We get rid of parentheses

4x^2+12x+1x-1-1=0

We add all the numbers together, and all the variables

4x^2+13x-2=0

a = 4; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·4·(-2)
Δ = 201
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{-(13)-\sqrt{201}}{2*4}=\frac{-13-\sqrt{201}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{201}}{2*4}=\frac{-13+\sqrt{201}}{8}
$