X-3/4x=45

Solution for X-3/4x=45 equation:

X-3/4X=45

We move all terms to the left:

X-3/4X-(45)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-45*4X-3=0

Wy multiply elements

4X^2-180X-3=0

a = 4; b = -180; c = -3;
Δ = b2-4ac
Δ = -1802-4·4·(-3)
Δ = 32448
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:

$\sqrt{\Delta}=\sqrt{32448}=\sqrt{10816*3}=\sqrt{10816}*\sqrt{3}=104\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-104\sqrt{3}}{2*4}=\frac{180-104\sqrt{3}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+104\sqrt{3}}{2*4}=\frac{180+104\sqrt{3}}{8}
$