X-3/4x=14

Solution for X-3/4x=14 equation:

X-3/4X=14

We move all terms to the left:

X-3/4X-(14)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-14*4X-3=0

Wy multiply elements

4X^2-56X-3=0

a = 4; b = -56; c = -3;
Δ = b2-4ac
Δ = -562-4·4·(-3)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{199}}{2*4}=\frac{56-4\sqrt{199}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{199}}{2*4}=\frac{56+4\sqrt{199}}{8}
$