2x-3-x2+17x-2=-7

Solution for 2x-3-x2+17x-2=-7 equation:

2x-3-x2+17x-2=-7

We move all terms to the left:

2x-3-x2+17x-2-(-7)=0

We add all the numbers together, and all the variables

-1x^2+19x+2=0

a = -1; b = 19; c = +2;
Δ = b2-4ac
Δ = 192-4·(-1)·2
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{41}}{2*-1}=\frac{-19-3\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{41}}{2*-1}=\frac{-19+3\sqrt{41}}{-2}
$