93=3x(2+5x)

Solution for 93=3x(2+5x) equation:

93=3x(2+5x)

We move all terms to the left:

93-(3x(2+5x))=0

We add all the numbers together, and all the variables

-(3x(5x+2))+93=0


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

3x(5x+2)

We multiply parentheses

15x^2+6x

Back to the equation:

-(15x^2+6x)


We get rid of parentheses

-15x^2-6x+93=0

a = -15; b = -6; c = +93;
Δ = b2-4ac
Δ = -62-4·(-15)·93
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{39}}{2*-15}=\frac{6-12\sqrt{39}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{39}}{2*-15}=\frac{6+12\sqrt{39}}{-30}
$