5x(x-3)-7(6-x)+29=50-3(8-x)

Solution for 5x(x-3)-7(6-x)+29=50-3(8-x) equation:

5x(x-3)-7(6-x)+29=50-3(8-x)

We move all terms to the left:

5x(x-3)-7(6-x)+29-(50-3(8-x))=0

We add all the numbers together, and all the variables

5x(x-3)-7(-1x+6)-(50-3(-1x+8))+29=0

We multiply parentheses

5x^2-15x+7x-(50-3(-1x+8))-42+29=0


We calculate terms in parentheses: -(50-3(-1x+8)), so:

50-3(-1x+8)

determiningTheFunctionDomain
-3(-1x+8)+50

We multiply parentheses

3x-24+50

We add all the numbers together, and all the variables

3x+26

Back to the equation:

-(3x+26)


We add all the numbers together, and all the variables

5x^2-8x-(3x+26)-13=0

We get rid of parentheses

5x^2-8x-3x-26-13=0

We add all the numbers together, and all the variables

5x^2-11x-39=0

a = 5; b = -11; c = -39;
Δ = b2-4ac
Δ = -112-4·5·(-39)
Δ = 901
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{-(-11)-\sqrt{901}}{2*5}=\frac{11-\sqrt{901}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{901}}{2*5}=\frac{11+\sqrt{901}}{10}
$