X+5/4(x)=6750

Solution for X+5/4(x)=6750 equation:

X+5/4(X)=6750

We move all terms to the left:

X+5/4(X)-(6750)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-6750*4X+5=0

Wy multiply elements

4X^2-27000X+5=0

a = 4; b = -27000; c = +5;
Δ = b2-4ac
Δ = -270002-4·4·5
Δ = 728999920
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:

$\sqrt{\Delta}=\sqrt{728999920}=\sqrt{16*45562495}=\sqrt{16}*\sqrt{45562495}=4\sqrt{45562495}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27000)-4\sqrt{45562495}}{2*4}=\frac{27000-4\sqrt{45562495}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27000)+4\sqrt{45562495}}{2*4}=\frac{27000+4\sqrt{45562495}}{8}
$