7.17x(x/3)+3(2x/3)=18(6/3)

Solution for 7.17x(x/3)+3(2x/3)=18(6/3) equation:

7.17x(x/3)+3(2x/3)=18(6/3)

We move all terms to the left:

7.17x(x/3)+3(2x/3)-(18(6/3))=0

We add all the numbers together, and all the variables

7.17x(+x/3)+3(+2x/3)-(182)=0

We add all the numbers together, and all the variables

7.17x(+x/3)+3(+2x/3)-182=0

We multiply parentheses

7x^2+6x-182=0

a = 7; b = 6; c = -182;
Δ = b2-4ac
Δ = 62-4·7·(-182)
Δ = 5132
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:

$\sqrt{\Delta}=\sqrt{5132}=\sqrt{4*1283}=\sqrt{4}*\sqrt{1283}=2\sqrt{1283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1283}}{2*7}=\frac{-6-2\sqrt{1283}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1283}}{2*7}=\frac{-6+2\sqrt{1283}}{14}
$