17x+47=2(6x+15)17x+47=2(6x+15)

Solution for 17x+47=2(6x+15)17x+47=2(6x+15) equation:

17x+47=2(6x+15)17x+47=2(6x+15)

We move all terms to the left:

17x+47-(2(6x+15)17x+47)=0


We calculate terms in parentheses: -(2(6x+15)17x+47), so:

2(6x+15)17x+47

We multiply parentheses

204x^2+510x+47

Back to the equation:

-(204x^2+510x+47)


We get rid of parentheses

-204x^2+17x-510x-47+47=0

We add all the numbers together, and all the variables

-204x^2-493x=0

a = -204; b = -493; c = 0;
Δ = b2-4ac
Δ = -4932-4·(-204)·0
Δ = 243049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{243049}=493$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-493)-493}{2*-204}=\frac{0}{-408}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-493)+493}{2*-204}=\frac{986}{-408}
=-2+5/12
$