-14=-5x(x-4)+9(x-6)

Solution for -14=-5x(x-4)+9(x-6) equation:

-14=-5x(x-4)+9(x-6)

We move all terms to the left:

-14-(-5x(x-4)+9(x-6))=0


We calculate terms in parentheses: -(-5x(x-4)+9(x-6)), so:

-5x(x-4)+9(x-6)

We multiply parentheses

-5x^2+20x+9x-54

We add all the numbers together, and all the variables

-5x^2+29x-54

Back to the equation:

-(-5x^2+29x-54)


We get rid of parentheses

5x^2-29x+54-14=0

We add all the numbers together, and all the variables

5x^2-29x+40=0

a = 5; b = -29; c = +40;
Δ = b2-4ac
Δ = -292-4·5·40
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{41}}{2*5}=\frac{29-\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{41}}{2*5}=\frac{29+\sqrt{41}}{10}
$