7x-4/5x+2-2=10

Solution for 7x-4/5x+2-2=10 equation:

7x-4/5x+2-2=10

We move all terms to the left:

7x-4/5x+2-2-(10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7x-4/5x-10=0

We multiply all the terms by the denominator


7x*5x-10*5x-4=0

Wy multiply elements

35x^2-50x-4=0

a = 35; b = -50; c = -4;
Δ = b2-4ac
Δ = -502-4·35·(-4)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{85}}{2*35}=\frac{50-6\sqrt{85}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{85}}{2*35}=\frac{50+6\sqrt{85}}{70}
$