23x+5=-12x2

Solution for 23x+5=-12x2 equation:

23x+5=-12x^2

We move all terms to the left:

23x+5-(-12x^2)=0

We get rid of parentheses

12x^2+23x+5=0

a = 12; b = 23; c = +5;
Δ = b2-4ac
Δ = 232-4·12·5
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*12}=\frac{-40}{24}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*12}=\frac{-6}{24}
=-1/4
$