14+5=5x-6(-3x+15)+57x-9x2=5x-6

Solution for 14+5=5x-6(-3x+15)+57x-9x2=5x-6 equation:

14+5=5x-6(-3x+15)+57x-9x^2=5x-6

We move all terms to the left:

14+5-(5x-6(-3x+15)+57x-9x^2)=0

We add all the numbers together, and all the variables

-(5x-6(-3x+15)+57x-9x^2)+19=0


We calculate terms in parentheses: -(5x-6(-3x+15)+57x-9x^2), so:

5x-6(-3x+15)+57x-9x^2

determiningTheFunctionDomain
-9x^2+5x-6(-3x+15)+57x

We add all the numbers together, and all the variables

-9x^2+62x-6(-3x+15)

We multiply parentheses

-9x^2+62x+18x-90

We add all the numbers together, and all the variables

-9x^2+80x-90

Back to the equation:

-(-9x^2+80x-90)


We get rid of parentheses

9x^2-80x+90+19=0

We add all the numbers together, and all the variables

9x^2-80x+109=0

a = 9; b = -80; c = +109;
Δ = b2-4ac
Δ = -802-4·9·109
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{619}}{2*9}=\frac{80-2\sqrt{619}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{619}}{2*9}=\frac{80+2\sqrt{619}}{18}
$