(x+7)(2x-3)=-21

Solution for (x+7)(2x-3)=-21 equation:

(x+7)(2x-3)=-21

We move all terms to the left:

(x+7)(2x-3)-(-21)=0

We add all the numbers together, and all the variables

(x+7)(2x-3)+21=0

We multiply parentheses ..

(+2x^2-3x+14x-21)+21=0

We get rid of parentheses

2x^2-3x+14x-21+21=0

We add all the numbers together, and all the variables

2x^2+11x=0

a = 2; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·2·0
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{-(11)-11}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*2}=\frac{0}{4}
=0
$