19x+10=-7x^2

Solution for 19x+10=-7x^2 equation:

19x+10=-7x^2

We move all terms to the left:

19x+10-(-7x^2)=0

We get rid of parentheses

7x^2+19x+10=0

a = 7; b = 19; c = +10;
Δ = b2-4ac
Δ = 192-4·7·10
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{-(19)-9}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+9}{2*7}=\frac{-10}{14}
=-5/7
$