X^2+(x+5)=65

Solution for X^2+(x+5)=65 equation:

X^2+(X+5)=65

We move all terms to the left:

X^2+(X+5)-(65)=0

We get rid of parentheses

X^2+X+5-65=0

We add all the numbers together, and all the variables

X^2+X-60=0

a = 1; b = 1; c = -60;
Δ = b2-4ac
Δ = 12-4·1·(-60)
Δ = 241
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{-(1)-\sqrt{241}}{2*1}=\frac{-1-\sqrt{241}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*1}=\frac{-1+\sqrt{241}}{2}
$