12x2-7x=-1

Solution for 12x2-7x=-1 equation:

12x^2-7x=-1

We move all terms to the left:

12x^2-7x-(-1)=0

We add all the numbers together, and all the variables

12x^2-7x+1=0

a = 12; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·12·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*12}=\frac{6}{24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*12}=\frac{8}{24}
=1/3
$