5x(1+3x)=10

Solution for 5x(1+3x)=10 equation:

5x(1+3x)=10

We move all terms to the left:

5x(1+3x)-(10)=0

We add all the numbers together, and all the variables

5x(3x+1)-10=0

We multiply parentheses

15x^2+5x-10=0

a = 15; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·15·(-10)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*15}=\frac{-30}{30}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*15}=\frac{20}{30}
=2/3
$