X+3/4*x=150

Solution for X+3/4*x=150 equation:

X+3/4X=150

We move all terms to the left:

X+3/4X-(150)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-150*4X+3=0

Wy multiply elements

4X^2-600X+3=0

a = 4; b = -600; c = +3;
Δ = b2-4ac
Δ = -6002-4·4·3
Δ = 359952
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:

$\sqrt{\Delta}=\sqrt{359952}=\sqrt{16*22497}=\sqrt{16}*\sqrt{22497}=4\sqrt{22497}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-4\sqrt{22497}}{2*4}=\frac{600-4\sqrt{22497}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+4\sqrt{22497}}{2*4}=\frac{600+4\sqrt{22497}}{8}
$