7/4(x)+x=33

Solution for 7/4(x)+x=33 equation:

7/4(x)+x=33

We move all terms to the left:

7/4(x)+x-(33)=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+7/4x-33=0

We multiply all the terms by the denominator


x*4x-33*4x+7=0

Wy multiply elements

4x^2-132x+7=0

a = 4; b = -132; c = +7;
Δ = b2-4ac
Δ = -1322-4·4·7
Δ = 17312
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:

$\sqrt{\Delta}=\sqrt{17312}=\sqrt{16*1082}=\sqrt{16}*\sqrt{1082}=4\sqrt{1082}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1082}}{2*4}=\frac{132-4\sqrt{1082}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1082}}{2*4}=\frac{132+4\sqrt{1082}}{8}
$