(x+5)(5x+2)=-16

Solution for (x+5)(5x+2)=-16 equation:

(x+5)(5x+2)=-16

We move all terms to the left:

(x+5)(5x+2)-(-16)=0

We add all the numbers together, and all the variables

(x+5)(5x+2)+16=0

We multiply parentheses ..

(+5x^2+2x+25x+10)+16=0

We get rid of parentheses

5x^2+2x+25x+10+16=0

We add all the numbers together, and all the variables

5x^2+27x+26=0

a = 5; b = 27; c = +26;
Δ = b2-4ac
Δ = 272-4·5·26
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{209}}{2*5}=\frac{-27-\sqrt{209}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{209}}{2*5}=\frac{-27+\sqrt{209}}{10}
$