12(x*x)=5-13x

Solution for 12(x*x)=5-13x equation:

12(x*x)=5-13x

We move all terms to the left:

12(x*x)-(5-13x)=0

We add all the numbers together, and all the variables

12(+x*x)-(-13x+5)=0

We multiply parentheses

12x^2-(-13x+5)=0

We get rid of parentheses

12x^2+13x-5=0

a = 12; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·12·(-5)
Δ = 409
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{-(13)-\sqrt{409}}{2*12}=\frac{-13-\sqrt{409}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{409}}{2*12}=\frac{-13+\sqrt{409}}{24}
$