2x-7=8x-47(3x-14)/2

Solution for 2x-7=8x-47(3x-14)/2 equation:

2x-7=8x-47(3x-14)/2

We move all terms to the left:

2x-7-(8x-47(3x-14)/2)=0

We multiply all the terms by the denominator


2x*2)-(8x-47(3x-14)-7*2)=0

We add all the numbers together, and all the variables

2x*2)-(8x-47(3x-14)=0

We multiply parentheses

2x*2)-(8x-141x+658=0

Wy multiply elements

4x^2-141x+658=0

a = 4; b = -141; c = +658;
Δ = b2-4ac
Δ = -1412-4·4·658
Δ = 9353
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-141)-\sqrt{9353}}{2*4}=\frac{141-\sqrt{9353}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-141)+\sqrt{9353}}{2*4}=\frac{141+\sqrt{9353}}{8}
$