8/9xX.10=2x-13

Solution for 8/9xX.10=2x-13 equation:

8/9xx.10=2x-13

We move all terms to the left:

8/9xx.10-(2x-13)=0


Domain of the equation: 9xx.10!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

8/9xx.10-2x+13=0

We multiply all the terms by the denominator


-2x*9xx.10+13*9xx.10+8=0

Wy multiply elements

-18x^2+117x+8=0

a = -18; b = 117; c = +8;
Δ = b2-4ac
Δ = 1172-4·(-18)·8
Δ = 14265
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:

$\sqrt{\Delta}=\sqrt{14265}=\sqrt{9*1585}=\sqrt{9}*\sqrt{1585}=3\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(117)-3\sqrt{1585}}{2*-18}=\frac{-117-3\sqrt{1585}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+3\sqrt{1585}}{2*-18}=\frac{-117+3\sqrt{1585}}{-36}
$