(2x-3)(x+1)=17

Solution for (2x-3)(x+1)=17 equation:

(2x-3)(x+1)=17

We move all terms to the left:

(2x-3)(x+1)-(17)=0

We multiply parentheses ..

(+2x^2+2x-3x-3)-17=0

We get rid of parentheses

2x^2+2x-3x-3-17=0

We add all the numbers together, and all the variables

2x^2-1x-20=0

a = 2; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·2·(-20)
Δ = 161
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{-(-1)-\sqrt{161}}{2*2}=\frac{1-\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*2}=\frac{1+\sqrt{161}}{4}
$