-9(3x+10)+x2=3(-6x+10)-9x+1

Solution for -9(3x+10)+x2=3(-6x+10)-9x+1 equation:

-9(3x+10)+x2=3(-6x+10)-9x+1

We move all terms to the left:

-9(3x+10)+x2-(3(-6x+10)-9x+1)=0

We add all the numbers together, and all the variables

x^2-9(3x+10)-(3(-6x+10)-9x+1)=0

We multiply parentheses

x^2-27x-(3(-6x+10)-9x+1)-90=0


We calculate terms in parentheses: -(3(-6x+10)-9x+1), so:

3(-6x+10)-9x+1

We add all the numbers together, and all the variables

-9x+3(-6x+10)+1

We multiply parentheses

-9x-18x+30+1

We add all the numbers together, and all the variables

-27x+31

Back to the equation:

-(-27x+31)


We get rid of parentheses

x^2-27x+27x-31-90=0

We add all the numbers together, and all the variables

x^2-121=0

a = 1; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·1·(-121)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22}{2*1}=\frac{22}{2}
=11
$