2x(17/61)+2x=34

Solution for 2x(17/61)+2x=34 equation:

2x(17/61)+2x=34

We move all terms to the left:

2x(17/61)+2x-(34)=0

We add all the numbers together, and all the variables

2x(+17/61)+2x-34=0

We add all the numbers together, and all the variables

2x+2x(+17/61)-34=0

We multiply parentheses

34x^2+2x-34=0

a = 34; b = 2; c = -34;
Δ = b2-4ac
Δ = 22-4·34·(-34)
Δ = 4628
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:

$\sqrt{\Delta}=\sqrt{4628}=\sqrt{4*1157}=\sqrt{4}*\sqrt{1157}=2\sqrt{1157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1157}}{2*34}=\frac{-2-2\sqrt{1157}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1157}}{2*34}=\frac{-2+2\sqrt{1157}}{68}
$