x(7x-17)=12

Solution for x(7x-17)=12 equation:

x(7x-17)=12

We move all terms to the left:

x(7x-17)-(12)=0

We multiply parentheses

7x^2-17x-12=0

a = 7; b = -17; c = -12;
Δ = b2-4ac
Δ = -172-4·7·(-12)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-25}{2*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*7}=\frac{42}{14}
=3
$