-(11x-13)+45-x=3(6-9x)17x+10

Solution for -(11x-13)+45-x=3(6-9x)17x+10 equation:

-(11x-13)+45-x=3(6-9x)17x+10

We move all terms to the left:

-(11x-13)+45-x-(3(6-9x)17x+10)=0

We add all the numbers together, and all the variables

-(11x-13)-x-(3(-9x+6)17x+10)+45=0

We add all the numbers together, and all the variables

-1x-(11x-13)-(3(-9x+6)17x+10)+45=0

We get rid of parentheses

-1x-11x-(3(-9x+6)17x+10)+13+45=0


We calculate terms in parentheses: -(3(-9x+6)17x+10), so:

3(-9x+6)17x+10

We multiply parentheses

-459x^2+306x+10

Back to the equation:

-(-459x^2+306x+10)


We add all the numbers together, and all the variables

-(-459x^2+306x+10)-12x+58=0

We get rid of parentheses

459x^2-306x-12x-10+58=0

We add all the numbers together, and all the variables

459x^2-318x+48=0

a = 459; b = -318; c = +48;
Δ = b2-4ac
Δ = -3182-4·459·48
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-318)-114}{2*459}=\frac{204}{918}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-318)+114}{2*459}=\frac{432}{918}
=8/17
$