x(6x-17)=28

Solution for x(6x-17)=28 equation:

x(6x-17)=28

We move all terms to the left:

x(6x-17)-(28)=0

We multiply parentheses

6x^2-17x-28=0

a = 6; b = -17; c = -28;
Δ = b2-4ac
Δ = -172-4·6·(-28)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-31}{2*6}=\frac{-14}{12}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+31}{2*6}=\frac{48}{12}
=4
$