17x+11=x^2+17x-38

Solution for 17x+11=x^2+17x-38 equation:

17x+11=x^2+17x-38

We move all terms to the left:

17x+11-(x^2+17x-38)=0

We get rid of parentheses

-x^2+17x-17x+38+11=0

We add all the numbers together, and all the variables

-1x^2+49=0

a = -1; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-1)·49
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-1}=\frac{14}{-2}
=-7
$