14x^2-67x=-6

Solution for 14x^2-67x=-6 equation:

14x^2-67x=-6

We move all terms to the left:

14x^2-67x-(-6)=0

We add all the numbers together, and all the variables

14x^2-67x+6=0

a = 14; b = -67; c = +6;
Δ = b2-4ac
Δ = -672-4·14·6
Δ = 4153
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{-(-67)-\sqrt{4153}}{2*14}=\frac{67-\sqrt{4153}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+\sqrt{4153}}{2*14}=\frac{67+\sqrt{4153}}{28}
$