10x^2+30=-40x

Solution for 10x^2+30=-40x equation:

10x^2+30=-40x

We move all terms to the left:

10x^2+30-(-40x)=0

We get rid of parentheses

10x^2+40x+30=0

a = 10; b = 40; c = +30;
Δ = b2-4ac
Δ = 402-4·10·30
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20}{2*10}=\frac{-20}{20}
=-1
$