7x-8=50/9x-6=40

Solution for 7x-8=50/9x-6=40 equation:

7x-8=50/9x-6=40

We move all terms to the left:

7x-8-(50/9x-6)=0


Domain of the equation: 9x-6)!=0

x∈R


We get rid of parentheses

7x-50/9x+6-8=0

We multiply all the terms by the denominator


7x*9x+6*9x-8*9x-50=0

Wy multiply elements

63x^2+54x-72x-50=0

We add all the numbers together, and all the variables

63x^2-18x-50=0

a = 63; b = -18; c = -50;
Δ = b2-4ac
Δ = -182-4·63·(-50)
Δ = 12924
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:

$\sqrt{\Delta}=\sqrt{12924}=\sqrt{36*359}=\sqrt{36}*\sqrt{359}=6\sqrt{359}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{359}}{2*63}=\frac{18-6\sqrt{359}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{359}}{2*63}=\frac{18+6\sqrt{359}}{126}
$