x^2+27x+21=5x-19

Solution for x^2+27x+21=5x-19 equation:

x^2+27x+21=5x-19

We move all terms to the left:

x^2+27x+21-(5x-19)=0

We get rid of parentheses

x^2+27x-5x+19+21=0

We add all the numbers together, and all the variables

x^2+22x+40=0

a = 1; b = 22; c = +40;
Δ = b2-4ac
Δ = 222-4·1·40
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*1}=\frac{-4}{2}
=-2
$