3/4x-1+x=153

Solution for 3/4x-1+x=153 equation:

3/4x-1+x=153

We move all terms to the left:

3/4x-1+x-(153)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-154=0

We multiply all the terms by the denominator


x*4x-154*4x+3=0

Wy multiply elements

4x^2-616x+3=0

a = 4; b = -616; c = +3;
Δ = b2-4ac
Δ = -6162-4·4·3
Δ = 379408
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:

$\sqrt{\Delta}=\sqrt{379408}=\sqrt{16*23713}=\sqrt{16}*\sqrt{23713}=4\sqrt{23713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-616)-4\sqrt{23713}}{2*4}=\frac{616-4\sqrt{23713}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-616)+4\sqrt{23713}}{2*4}=\frac{616+4\sqrt{23713}}{8}
$