(x-1)(2x+5)=9

Solution for (x-1)(2x+5)=9 equation:

(x-1)(2x+5)=9

We move all terms to the left:

(x-1)(2x+5)-(9)=0

We multiply parentheses ..

(+2x^2+5x-2x-5)-9=0

We get rid of parentheses

2x^2+5x-2x-5-9=0

We add all the numbers together, and all the variables

2x^2+3x-14=0

a = 2; b = 3; c = -14;
Δ = b2-4ac
Δ = 32-4·2·(-14)
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{-(3)-11}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*2}=\frac{8}{4}
=2
$