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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

2x^2-14x+3x-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{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*2}=\frac{22}{4}
=5+1/2
$