(2x-1)(x+3)=x+67

Solution for (2x-1)(x+3)=x+67 equation:

(2x-1)(x+3)=x+67

We move all terms to the left:

(2x-1)(x+3)-(x+67)=0

We get rid of parentheses

(2x-1)(x+3)-x-67=0

We multiply parentheses ..

(+2x^2+6x-1x-3)-x-67=0

We add all the numbers together, and all the variables

(+2x^2+6x-1x-3)-1x-67=0

We get rid of parentheses

2x^2+6x-1x-1x-3-67=0

We add all the numbers together, and all the variables

2x^2+4x-70=0

a = 2; b = 4; c = -70;
Δ = b2-4ac
Δ = 42-4·2·(-70)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-24}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+24}{2*2}=\frac{20}{4}
=5
$