7x^2-12x+13x=14

Solution for 7x^2-12x+13x=14 equation:

7x^2-12x+13x=14

We move all terms to the left:

7x^2-12x+13x-(14)=0

We add all the numbers together, and all the variables

7x^2+x-14=0

a = 7; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·7·(-14)
Δ = 393
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{-(1)-\sqrt{393}}{2*7}=\frac{-1-\sqrt{393}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{393}}{2*7}=\frac{-1+\sqrt{393}}{14}
$