3/4x+15=45-4x+3

Solution for 3/4x+15=45-4x+3 equation:

3/4x+15=45-4x+3

We move all terms to the left:

3/4x+15-(45-4x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-4x+48)+15=0

We get rid of parentheses

3/4x+4x-48+15=0

We multiply all the terms by the denominator


4x*4x-48*4x+15*4x+3=0

Wy multiply elements

16x^2-192x+60x+3=0

We add all the numbers together, and all the variables

16x^2-132x+3=0

a = 16; b = -132; c = +3;
Δ = b2-4ac
Δ = -1322-4·16·3
Δ = 17232
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:

$\sqrt{\Delta}=\sqrt{17232}=\sqrt{16*1077}=\sqrt{16}*\sqrt{1077}=4\sqrt{1077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1077}}{2*16}=\frac{132-4\sqrt{1077}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1077}}{2*16}=\frac{132+4\sqrt{1077}}{32}
$