-9x-2x(x-9)=-8(x+9)+3

Solution for -9x-2x(x-9)=-8(x+9)+3 equation:

-9x-2x(x-9)=-8(x+9)+3

We move all terms to the left:

-9x-2x(x-9)-(-8(x+9)+3)=0

We multiply parentheses

-2x^2-9x+18x-(-8(x+9)+3)=0


We calculate terms in parentheses: -(-8(x+9)+3), so:

-8(x+9)+3

We multiply parentheses

-8x-72+3

We add all the numbers together, and all the variables

-8x-69

Back to the equation:

-(-8x-69)


We add all the numbers together, and all the variables

-2x^2+9x-(-8x-69)=0

We get rid of parentheses

-2x^2+9x+8x+69=0

We add all the numbers together, and all the variables

-2x^2+17x+69=0

a = -2; b = 17; c = +69;
Δ = b2-4ac
Δ = 172-4·(-2)·69
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-29}{2*-2}=\frac{-46}{-4}
=11+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+29}{2*-2}=\frac{12}{-4}
=-3
$