5x^2+16x+8=13-4x

Solution for 5x^2+16x+8=13-4x equation:

5x^2+16x+8=13-4x

We move all terms to the left:

5x^2+16x+8-(13-4x)=0

We add all the numbers together, and all the variables

5x^2+16x-(-4x+13)+8=0

We get rid of parentheses

5x^2+16x+4x-13+8=0

We add all the numbers together, and all the variables

5x^2+20x-5=0

a = 5; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·5·(-5)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{5}}{2*5}=\frac{-20-10\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{5}}{2*5}=\frac{-20+10\sqrt{5}}{10}
$