7/6x=10-17x

Solution for 7/6x=10-17x equation:

7/6x=10-17x

We move all terms to the left:

7/6x-(10-17x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7/6x-(-17x+10)=0

We get rid of parentheses

7/6x+17x-10=0

We multiply all the terms by the denominator


17x*6x-10*6x+7=0

Wy multiply elements

102x^2-60x+7=0

a = 102; b = -60; c = +7;
Δ = b2-4ac
Δ = -602-4·102·7
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{186}}{2*102}=\frac{60-2\sqrt{186}}{204}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{186}}{2*102}=\frac{60+2\sqrt{186}}{204}
$