4(3x-12)=14-(5x+8)x=3+3/17

Solution for 4(3x-12)=14-(5x+8)x=3+3/17 equation:

4(3x-12)=14-(5x+8)x=3+3/17

We move all terms to the left:

4(3x-12)-(14-(5x+8)x)=0

We multiply parentheses

12x-(14-(5x+8)x)-48=0


We calculate terms in parentheses: -(14-(5x+8)x), so:

14-(5x+8)x

determiningTheFunctionDomain
-(5x+8)x+14

We multiply parentheses

-5x^2-8x+14

Back to the equation:

-(-5x^2-8x+14)


We get rid of parentheses

5x^2+8x+12x-14-48=0

We add all the numbers together, and all the variables

5x^2+20x-62=0

a = 5; b = 20; c = -62;
Δ = b2-4ac
Δ = 202-4·5·(-62)
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{410}}{2*5}=\frac{-20-2\sqrt{410}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{410}}{2*5}=\frac{-20+2\sqrt{410}}{10}
$