X+3/4x=34

Solution for X+3/4x=34 equation:

X+3/4X=34

We move all terms to the left:

X+3/4X-(34)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-34*4X+3=0

Wy multiply elements

4X^2-136X+3=0

a = 4; b = -136; c = +3;
Δ = b2-4ac
Δ = -1362-4·4·3
Δ = 18448
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:

$\sqrt{\Delta}=\sqrt{18448}=\sqrt{16*1153}=\sqrt{16}*\sqrt{1153}=4\sqrt{1153}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{1153}}{2*4}=\frac{136-4\sqrt{1153}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{1153}}{2*4}=\frac{136+4\sqrt{1153}}{8}
$