X+3/4x=350

Solution for X+3/4x=350 equation:

X+3/4X=350

We move all terms to the left:

X+3/4X-(350)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-350*4X+3=0

Wy multiply elements

4X^2-1400X+3=0

a = 4; b = -1400; c = +3;
Δ = b2-4ac
Δ = -14002-4·4·3
Δ = 1959952
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:

$\sqrt{\Delta}=\sqrt{1959952}=\sqrt{16*122497}=\sqrt{16}*\sqrt{122497}=4\sqrt{122497}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-4\sqrt{122497}}{2*4}=\frac{1400-4\sqrt{122497}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+4\sqrt{122497}}{2*4}=\frac{1400+4\sqrt{122497}}{8}
$