23x+6=-15x^2

Solution for 23x+6=-15x^2 equation:

23x+6=-15x^2

We move all terms to the left:

23x+6-(-15x^2)=0

We get rid of parentheses

15x^2+23x+6=0

a = 15; b = 23; c = +6;
Δ = b2-4ac
Δ = 232-4·15·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-13}{2*15}=\frac{-36}{30}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+13}{2*15}=\frac{-10}{30}
=-1/3
$