6x^2=17x-3

Solution for 6x^2=17x-3 equation:

6x^2=17x-3

We move all terms to the left:

6x^2-(17x-3)=0

We get rid of parentheses

6x^2-17x+3=0

a = 6; b = -17; c = +3;
Δ = b2-4ac
Δ = -172-4·6·3
Δ = 217
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{217}}{2*6}=\frac{17-\sqrt{217}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{217}}{2*6}=\frac{17+\sqrt{217}}{12}
$