5x(x+6)=-2x(x+6)+28

Solution for 5x(x+6)=-2x(x+6)+28 equation:

5x(x+6)=-2x(x+6)+28

We move all terms to the left:

5x(x+6)-(-2x(x+6)+28)=0

We multiply parentheses

5x^2+30x-(-2x(x+6)+28)=0


We calculate terms in parentheses: -(-2x(x+6)+28), so:

-2x(x+6)+28

We multiply parentheses

-2x^2-12x+28

Back to the equation:

-(-2x^2-12x+28)


We get rid of parentheses

5x^2+2x^2+12x+30x-28=0

We add all the numbers together, and all the variables

7x^2+42x-28=0

a = 7; b = 42; c = -28;
Δ = b2-4ac
Δ = 422-4·7·(-28)
Δ = 2548
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:

$\sqrt{\Delta}=\sqrt{2548}=\sqrt{196*13}=\sqrt{196}*\sqrt{13}=14\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14\sqrt{13}}{2*7}=\frac{-42-14\sqrt{13}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14\sqrt{13}}{2*7}=\frac{-42+14\sqrt{13}}{14}
$