(2x+7)(x-3)+18=0

Solution for (2x+7)(x-3)+18=0 equation:

(2x+7)(x-3)+18=0

We multiply parentheses ..

(+2x^2-6x+7x-21)+18=0

We get rid of parentheses

2x^2-6x+7x-21+18=0

We add all the numbers together, and all the variables

2x^2+x-3=0

a = 2; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·2·(-3)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*2}=\frac{4}{4}
=1
$