21x+9=-10x^2

Solution for 21x+9=-10x^2 equation:

21x+9=-10x^2

We move all terms to the left:

21x+9-(-10x^2)=0

We get rid of parentheses

10x^2+21x+9=0

a = 10; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·10·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*10}=\frac{-12}{20}
=-3/5
$