(x+3)(x-1)+(x+1)(3x)=83

Solution for (x+3)(x-1)+(x+1)(3x)=83 equation:

(x+3)(x-1)+(x+1)(3x)=83

We move all terms to the left:

(x+3)(x-1)+(x+1)(3x)-(83)=0

We multiply parentheses

3x^2+(x+3)(x-1)+3x-83=0

We multiply parentheses ..

3x^2+(+x^2-1x+3x-3)+3x-83=0

We get rid of parentheses

3x^2+x^2-1x+3x+3x-3-83=0

We add all the numbers together, and all the variables

4x^2+5x-86=0

a = 4; b = 5; c = -86;
Δ = b2-4ac
Δ = 52-4·4·(-86)
Δ = 1401
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{1401}}{2*4}=\frac{-5-\sqrt{1401}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1401}}{2*4}=\frac{-5+\sqrt{1401}}{8}
$