(x*x)+17x+19=6x-5

Solution for (x*x)+17x+19=6x-5 equation:

(x*x)+17x+19=6x-5

We move all terms to the left:

(x*x)+17x+19-(6x-5)=0

We add all the numbers together, and all the variables

(+x*x)+17x-(6x-5)+19=0

We add all the numbers together, and all the variables

17x+(+x*x)-(6x-5)+19=0

We get rid of parentheses

17x+x*x-6x+5+19=0

We add all the numbers together, and all the variables

11x+x*x+24=0

Wy multiply elements

x^2+11x+24=0

a = 1; b = 11; c = +24;
Δ = b2-4ac
Δ = 112-4·1·24
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{-(11)-5}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*1}=\frac{-6}{2}
=-3
$