3/4x+2x+7=34.5

Solution for 3/4x+2x+7=34.5 equation:

3/4x+2x+7=34.5

We move all terms to the left:

3/4x+2x+7-(34.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-27.5=0

We multiply all the terms by the denominator


2x*4x-(27.5)*4x+3=0

We multiply parentheses

2x*4x-110x+3=0

Wy multiply elements

8x^2-110x+3=0

a = 8; b = -110; c = +3;
Δ = b2-4ac
Δ = -1102-4·8·3
Δ = 12004
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:

$\sqrt{\Delta}=\sqrt{12004}=\sqrt{4*3001}=\sqrt{4}*\sqrt{3001}=2\sqrt{3001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3001}}{2*8}=\frac{110-2\sqrt{3001}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3001}}{2*8}=\frac{110+2\sqrt{3001}}{16}
$