3/4x+8=5x-14

Solution for 3/4x+8=5x-14 equation:

3/4x+8=5x-14

We move all terms to the left:

3/4x+8-(5x-14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-5x+14+8=0

We multiply all the terms by the denominator


-5x*4x+14*4x+8*4x+3=0

Wy multiply elements

-20x^2+56x+32x+3=0

We add all the numbers together, and all the variables

-20x^2+88x+3=0

a = -20; b = 88; c = +3;
Δ = b2-4ac
Δ = 882-4·(-20)·3
Δ = 7984
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:

$\sqrt{\Delta}=\sqrt{7984}=\sqrt{16*499}=\sqrt{16}*\sqrt{499}=4\sqrt{499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{499}}{2*-20}=\frac{-88-4\sqrt{499}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{499}}{2*-20}=\frac{-88+4\sqrt{499}}{-40}
$