1=5x(3x+2)

Solution for 1=5x(3x+2) equation:

1=5x(3x+2)

We move all terms to the left:

1-(5x(3x+2))=0


We calculate terms in parentheses: -(5x(3x+2)), so:

5x(3x+2)

We multiply parentheses

15x^2+10x

Back to the equation:

-(15x^2+10x)


We get rid of parentheses

-15x^2-10x+1=0

a = -15; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-15)·1
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{10}}{2*-15}=\frac{10-4\sqrt{10}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{10}}{2*-15}=\frac{10+4\sqrt{10}}{-30}
$