5x^2+15x+x+3=0

Solution for 5x^2+15x+x+3=0 equation:

5x^2+15x+x+3=0

We add all the numbers together, and all the variables

5x^2+16x+3=0

a = 5; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·5·3
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-14}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+14}{2*5}=\frac{-2}{10}
=-1/5
$