12x^2=-7x-1

Solution for 12x^2=-7x-1 equation:

12x^2=-7x-1

We move all terms to the left:

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

We get rid of parentheses

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