5(x^2+11x+19)=0

Solution for 5(x^2+11x+19)=0 equation:

5(x^2+11x+19)=0

We multiply parentheses

5x^2+55x+95=0

a = 5; b = 55; c = +95;
Δ = b2-4ac
Δ = 552-4·5·95
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-15\sqrt{5}}{2*5}=\frac{-55-15\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+15\sqrt{5}}{2*5}=\frac{-55+15\sqrt{5}}{10}
$