(2x-1)(3x+1)=50

Solution for (2x-1)(3x+1)=50 equation:

(2x-1)(3x+1)=50

We move all terms to the left:

(2x-1)(3x+1)-(50)=0

We multiply parentheses ..

(+6x^2+2x-3x-1)-50=0

We get rid of parentheses

6x^2+2x-3x-1-50=0

We add all the numbers together, and all the variables

6x^2-1x-51=0

a = 6; b = -1; c = -51;
Δ = b2-4ac
Δ = -12-4·6·(-51)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*6}=\frac{-34}{12}
=-2+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*6}=\frac{36}{12}
=3
$