X-3/4x=91

Solution for X-3/4x=91 equation:

X-3/4X=91

We move all terms to the left:

X-3/4X-(91)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-91*4X-3=0

Wy multiply elements

4X^2-364X-3=0

a = 4; b = -364; c = -3;
Δ = b2-4ac
Δ = -3642-4·4·(-3)
Δ = 132544
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:

$\sqrt{\Delta}=\sqrt{132544}=\sqrt{64*2071}=\sqrt{64}*\sqrt{2071}=8\sqrt{2071}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-8\sqrt{2071}}{2*4}=\frac{364-8\sqrt{2071}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+8\sqrt{2071}}{2*4}=\frac{364+8\sqrt{2071}}{8}
$