3-23x=-14x(x-21)-15(x+33)

Solution for 3-23x=-14x(x-21)-15(x+33) equation:

3-23x=-14x(x-21)-15(x+33)

We move all terms to the left:

3-23x-(-14x(x-21)-15(x+33))=0


We calculate terms in parentheses: -(-14x(x-21)-15(x+33)), so:

-14x(x-21)-15(x+33)

We multiply parentheses

-14x^2+294x-15x-495

We add all the numbers together, and all the variables

-14x^2+279x-495

Back to the equation:

-(-14x^2+279x-495)


We get rid of parentheses

14x^2-279x-23x+495+3=0

We add all the numbers together, and all the variables

14x^2-302x+498=0

a = 14; b = -302; c = +498;
Δ = b2-4ac
Δ = -3022-4·14·498
Δ = 63316
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:

$\sqrt{\Delta}=\sqrt{63316}=\sqrt{4*15829}=\sqrt{4}*\sqrt{15829}=2\sqrt{15829}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-302)-2\sqrt{15829}}{2*14}=\frac{302-2\sqrt{15829}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-302)+2\sqrt{15829}}{2*14}=\frac{302+2\sqrt{15829}}{28}
$