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

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

5-(2X-1)(1+3X)=1

We move all terms to the left:

5-(2X-1)(1+3X)-(1)=0

We add all the numbers together, and all the variables

-(2X-1)(3X+1)+5-1=0

We add all the numbers together, and all the variables

-(2X-1)(3X+1)+4=0

We multiply parentheses ..

-(+6X^2+2X-3X-1)+4=0

We get rid of parentheses

-6X^2-2X+3X+1+4=0

We add all the numbers together, and all the variables

-6X^2+X+5=0

a = -6; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-6)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*-6}=\frac{-12}{-12}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-6}=\frac{10}{-12}
=-5/6
$