X+3/4x=35

Solution for X+3/4x=35 equation:

X+3/4X=35

We move all terms to the left:

X+3/4X-(35)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-35*4X+3=0

Wy multiply elements

4X^2-140X+3=0

a = 4; b = -140; c = +3;
Δ = b2-4ac
Δ = -1402-4·4·3
Δ = 19552
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:

$\sqrt{\Delta}=\sqrt{19552}=\sqrt{16*1222}=\sqrt{16}*\sqrt{1222}=4\sqrt{1222}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1222}}{2*4}=\frac{140-4\sqrt{1222}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1222}}{2*4}=\frac{140+4\sqrt{1222}}{8}
$