2x(1+5x)=15

Solution for 2x(1+5x)=15 equation:

2x(1+5x)=15

We move all terms to the left:

2x(1+5x)-(15)=0

We add all the numbers together, and all the variables

2x(5x+1)-15=0

We multiply parentheses

10x^2+2x-15=0

a = 10; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·10·(-15)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{151}}{2*10}=\frac{-2-2\sqrt{151}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{151}}{2*10}=\frac{-2+2\sqrt{151}}{20}
$