10x^2=-7-19x

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

10x^2=-7-19x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

10x^2+19x+7=0

a = 10; b = 19; c = +7;
Δ = b2-4ac
Δ = 192-4·10·7
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*10}=\frac{-28}{20}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+9}{2*10}=\frac{-10}{20}
=-1/2
$