7x-46/7x=4

Solution for 7x-46/7x=4 equation:

7x-46/7x=4

We move all terms to the left:

7x-46/7x-(4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


7x*7x-4*7x-46=0

Wy multiply elements

49x^2-28x-46=0

a = 49; b = -28; c = -46;
Δ = b2-4ac
Δ = -282-4·49·(-46)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-70\sqrt{2}}{2*49}=\frac{28-70\sqrt{2}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+70\sqrt{2}}{2*49}=\frac{28+70\sqrt{2}}{98}
$