2x-7/9x=10

Solution for 2x-7/9x=10 equation:

2x-7/9x=10

We move all terms to the left:

2x-7/9x-(10)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


2x*9x-10*9x-7=0

Wy multiply elements

18x^2-90x-7=0

a = 18; b = -90; c = -7;
Δ = b2-4ac
Δ = -902-4·18·(-7)
Δ = 8604
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:

$\sqrt{\Delta}=\sqrt{8604}=\sqrt{36*239}=\sqrt{36}*\sqrt{239}=6\sqrt{239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{239}}{2*18}=\frac{90-6\sqrt{239}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{239}}{2*18}=\frac{90+6\sqrt{239}}{36}
$