X^2+17-11=13x+10

Solution for X^2+17-11=13x+10 equation:

X^2+17-11=13X+10

We move all terms to the left:

X^2+17-11-(13X+10)=0

We add all the numbers together, and all the variables

X^2-(13X+10)+6=0

We get rid of parentheses

X^2-13X-10+6=0

We add all the numbers together, and all the variables

X^2-13X-4=0

a = 1; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·1·(-4)
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{185}}{2*1}=\frac{13-\sqrt{185}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{185}}{2*1}=\frac{13+\sqrt{185}}{2}
$