10+4x=5x(x+6)+33

Solution for 10+4x=5x(x+6)+33 equation:

10+4x=5x(x+6)+33

We move all terms to the left:

10+4x-(5x(x+6)+33)=0


We calculate terms in parentheses: -(5x(x+6)+33), so:

5x(x+6)+33

We multiply parentheses

5x^2+30x+33

Back to the equation:

-(5x^2+30x+33)


We get rid of parentheses

-5x^2+4x-30x-33+10=0

We add all the numbers together, and all the variables

-5x^2-26x-23=0

a = -5; b = -26; c = -23;
Δ = b2-4ac
Δ = -262-4·(-5)·(-23)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{6}}{2*-5}=\frac{26-6\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{6}}{2*-5}=\frac{26+6\sqrt{6}}{-10}
$