-2x+5x-9=3x(x-4)-5

Solution for -2x+5x-9=3x(x-4)-5 equation:

-2x+5x-9=3x(x-4)-5

We move all terms to the left:

-2x+5x-9-(3x(x-4)-5)=0

We add all the numbers together, and all the variables

3x-(3x(x-4)-5)-9=0


We calculate terms in parentheses: -(3x(x-4)-5), so:

3x(x-4)-5

We multiply parentheses

3x^2-12x-5

Back to the equation:

-(3x^2-12x-5)


We get rid of parentheses

-3x^2+3x+12x+5-9=0

We add all the numbers together, and all the variables

-3x^2+15x-4=0

a = -3; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·(-3)·(-4)
Δ = 177
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{-(15)-\sqrt{177}}{2*-3}=\frac{-15-\sqrt{177}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{177}}{2*-3}=\frac{-15+\sqrt{177}}{-6}
$