X=178-4(142-8x)/14

Solution for X=178-4(142-8x)/14 equation:

X=178-4(142-8X)/14

We move all terms to the left:

X-(178-4(142-8X)/14)=0

We add all the numbers together, and all the variables

X-(178-4(-8X+142)/14)=0

We multiply all the terms by the denominator


X*14)-(178-4(-8X+142)=0

We multiply parentheses

X*14)-(178+32X-568=0

Wy multiply elements

14X^2+32X-568=0

a = 14; b = 32; c = -568;
Δ = b2-4ac
Δ = 322-4·14·(-568)
Δ = 32832
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:

$\sqrt{\Delta}=\sqrt{32832}=\sqrt{576*57}=\sqrt{576}*\sqrt{57}=24\sqrt{57}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-24\sqrt{57}}{2*14}=\frac{-32-24\sqrt{57}}{28}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+24\sqrt{57}}{2*14}=\frac{-32+24\sqrt{57}}{28}
$