X+1/4x=750

Solution for X+1/4x=750 equation:

X+1/4X=750

We move all terms to the left:

X+1/4X-(750)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-750*4X+1=0

Wy multiply elements

4X^2-3000X+1=0

a = 4; b = -3000; c = +1;
Δ = b2-4ac
Δ = -30002-4·4·1
Δ = 8999984
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:

$\sqrt{\Delta}=\sqrt{8999984}=\sqrt{16*562499}=\sqrt{16}*\sqrt{562499}=4\sqrt{562499}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3000)-4\sqrt{562499}}{2*4}=\frac{3000-4\sqrt{562499}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3000)+4\sqrt{562499}}{2*4}=\frac{3000+4\sqrt{562499}}{8}
$