5x^2+30x+50=410

Solution for 5x^2+30x+50=410 equation:

5x^2+30x+50=410

We move all terms to the left:

5x^2+30x+50-(410)=0

We add all the numbers together, and all the variables

5x^2+30x-360=0

a = 5; b = 30; c = -360;
Δ = b2-4ac
Δ = 302-4·5·(-360)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-90}{2*5}=\frac{-120}{10}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+90}{2*5}=\frac{60}{10}
=6
$