2a^2=-19a-35

Solution for 2a^2=-19a-35 equation:

2a^2=-19a-35

We move all terms to the left:

2a^2-(-19a-35)=0

We get rid of parentheses

2a^2+19a+35=0

a = 2; b = 19; c = +35;
Δ = b2-4ac
Δ = 192-4·2·35
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-9}{2*2}=\frac{-28}{4}
=-7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+9}{2*2}=\frac{-10}{4}
=-2+1/2
$