3/4x+5=14x+15

Solution for 3/4x+5=14x+15 equation:

3/4x+5=14x+15

We move all terms to the left:

3/4x+5-(14x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-14x-15+5=0

We multiply all the terms by the denominator


-14x*4x-15*4x+5*4x+3=0

Wy multiply elements

-56x^2-60x+20x+3=0

We add all the numbers together, and all the variables

-56x^2-40x+3=0

a = -56; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-56)·3
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{142}}{2*-56}=\frac{40-4\sqrt{142}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{142}}{2*-56}=\frac{40+4\sqrt{142}}{-112}
$