7x-4/5x=8

Solution for 7x-4/5x=8 equation:

7x-4/5x=8

We move all terms to the left:

7x-4/5x-(8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


7x*5x-8*5x-4=0

Wy multiply elements

35x^2-40x-4=0

a = 35; b = -40; c = -4;
Δ = b2-4ac
Δ = -402-4·35·(-4)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{15}}{2*35}=\frac{40-12\sqrt{15}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{15}}{2*35}=\frac{40+12\sqrt{15}}{70}
$