x+6=5(60-x+6)x+6

Solution for x+6=5(60-x+6)x+6 equation:

x+6=5(60-x+6)x+6

We move all terms to the left:

x+6-(5(60-x+6)x+6)=0

We add all the numbers together, and all the variables

x-(5(-1x+66)x+6)+6=0


We calculate terms in parentheses: -(5(-1x+66)x+6), so:

5(-1x+66)x+6

We multiply parentheses

-5x^2+330x+6

Back to the equation:

-(-5x^2+330x+6)


We get rid of parentheses

5x^2-330x+x-6+6=0

We add all the numbers together, and all the variables

5x^2-329x=0

a = 5; b = -329; c = 0;
Δ = b2-4ac
Δ = -3292-4·5·0
Δ = 108241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108241}=329$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-329)-329}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-329)+329}{2*5}=\frac{658}{10}
=65+4/5
$