12x^2+31x*13=-7

Solution for 12x^2+31x*13=-7 equation:

12x^2+31x*13=-7

We move all terms to the left:

12x^2+31x*13-(-7)=0

We add all the numbers together, and all the variables

12x^2+31x*13+7=0

Wy multiply elements

12x^2+403x+7=0

a = 12; b = 403; c = +7;
Δ = b2-4ac
Δ = 4032-4·12·7
Δ = 162073
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{-(403)-\sqrt{162073}}{2*12}=\frac{-403-\sqrt{162073}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(403)+\sqrt{162073}}{2*12}=\frac{-403+\sqrt{162073}}{24}
$