x^2+18x-2x^2+60=17

Solution for x^2+18x-2x^2+60=17 equation:

x^2+18x-2x^2+60=17

We move all terms to the left:

x^2+18x-2x^2+60-(17)=0

We add all the numbers together, and all the variables

-1x^2+18x+43=0

a = -1; b = 18; c = +43;
Δ = b2-4ac
Δ = 182-4·(-1)·43
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{31}}{2*-1}=\frac{-18-4\sqrt{31}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{31}}{2*-1}=\frac{-18+4\sqrt{31}}{-2}
$