(X+1)=2x^2+5x-17

Solution for (X+1)=2x^2+5x-17 equation:

(X+1)=2X^2+5X-17

We move all terms to the left:

(X+1)-(2X^2+5X-17)=0

We get rid of parentheses

-2X^2+X-5X+1+17=0

We add all the numbers together, and all the variables

-2X^2-4X+18=0

a = -2; b = -4; c = +18;
Δ = b2-4ac
Δ = -42-4·(-2)·18
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*-2}=\frac{4-4\sqrt{10}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*-2}=\frac{4+4\sqrt{10}}{-4}
$