8x+(x*x)=2x+27

Solution for 8x+(x*x)=2x+27 equation:

8x+(x*x)=2x+27

We move all terms to the left:

8x+(x*x)-(2x+27)=0

We add all the numbers together, and all the variables

8x+(+x*x)-(2x+27)=0

We get rid of parentheses

8x+x*x-2x-27=0

We add all the numbers together, and all the variables

6x+x*x-27=0

Wy multiply elements

x^2+6x-27=0

a = 1; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*1}=\frac{6}{2}
=3
$