-2x+5x-17=3x(x-3)-31

Solution for -2x+5x-17=3x(x-3)-31 equation:

-2x+5x-17=3x(x-3)-31

We move all terms to the left:

-2x+5x-17-(3x(x-3)-31)=0

We add all the numbers together, and all the variables

3x-(3x(x-3)-31)-17=0


We calculate terms in parentheses: -(3x(x-3)-31), so:

3x(x-3)-31

We multiply parentheses

3x^2-9x-31

Back to the equation:

-(3x^2-9x-31)


We get rid of parentheses

-3x^2+3x+9x+31-17=0

We add all the numbers together, and all the variables

-3x^2+12x+14=0

a = -3; b = 12; c = +14;
Δ = b2-4ac
Δ = 122-4·(-3)·14
Δ = 312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{78}}{2*-3}=\frac{-12-2\sqrt{78}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{78}}{2*-3}=\frac{-12+2\sqrt{78}}{-6}
$