(1/6)=(15x-2x^2)/3

Solution for (1/6)=(15x-2x^2)/3 equation:

(1/6)=(15x-2x^2)/3

We move all terms to the left:

(1/6)-((15x-2x^2)/3)=0

We add all the numbers together, and all the variables

-((15x-2x^2)/3)+(+1/6)=0

We get rid of parentheses

-((15x-2x^2)/3)+1/6=0

We calculate fractions


(-((15x-2x^2)*6)/()+()/()=0


We calculate terms in parentheses: +(-((15x-2x^2)*6)/()+()/(), so:

-((15x-2x^2)*6)/()+()/(

We add all the numbers together, and all the variables

-((15x-2x^2)*6)/()+1

We multiply all the terms by the denominator


-((15x-2x^2)*6)+1*()


We calculate terms in parentheses: -((15x-2x^2)*6), so:

(15x-2x^2)*6

We multiply parentheses

-12x^2+90x

Back to the equation:

-(-12x^2+90x)


We add all the numbers together, and all the variables

-(-12x^2+90x)

We get rid of parentheses

12x^2-90x

Back to the equation:

+(12x^2-90x)


We get rid of parentheses

12x^2-90x=0

a = 12; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·12·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*12}=\frac{180}{24}
=7+1/2
$