x-7/4x=18

Solution for x-7/4x=18 equation:

x-7/4x=18

We move all terms to the left:

x-7/4x-(18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-18*4x-7=0

Wy multiply elements

4x^2-72x-7=0

a = 4; b = -72; c = -7;
Δ = b2-4ac
Δ = -722-4·4·(-7)
Δ = 5296
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:

$\sqrt{\Delta}=\sqrt{5296}=\sqrt{16*331}=\sqrt{16}*\sqrt{331}=4\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{331}}{2*4}=\frac{72-4\sqrt{331}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{331}}{2*4}=\frac{72+4\sqrt{331}}{8}
$