-3x2+17x-2=3

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

-3x^2+17x-2=3

We move all terms to the left:

-3x^2+17x-2-(3)=0

We add all the numbers together, and all the variables

-3x^2+17x-5=0

a = -3; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·(-3)·(-5)
Δ = 229
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{-(17)-\sqrt{229}}{2*-3}=\frac{-17-\sqrt{229}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{229}}{2*-3}=\frac{-17+\sqrt{229}}{-6}
$