(x+7)(4x+3)=-21

Solution for (x+7)(4x+3)=-21 equation:

(x+7)(4x+3)=-21

We move all terms to the left:

(x+7)(4x+3)-(-21)=0

We add all the numbers together, and all the variables

(x+7)(4x+3)+21=0

We multiply parentheses ..

(+4x^2+3x+28x+21)+21=0

We get rid of parentheses

4x^2+3x+28x+21+21=0

We add all the numbers together, and all the variables

4x^2+31x+42=0

a = 4; b = 31; c = +42;
Δ = b2-4ac
Δ = 312-4·4·42
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-17}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+17}{2*4}=\frac{-14}{8}
=-1+3/4
$