17-(3x-8)=2x(x-5)

Solution for 17-(3x-8)=2x(x-5) equation:

17-(3x-8)=2x(x-5)

We move all terms to the left:

17-(3x-8)-(2x(x-5))=0

We get rid of parentheses

-3x-(2x(x-5))+8+17=0


We calculate terms in parentheses: -(2x(x-5)), so:

2x(x-5)

We multiply parentheses

2x^2-10x

Back to the equation:

-(2x^2-10x)


We add all the numbers together, and all the variables

-3x-(2x^2-10x)+25=0

We get rid of parentheses

-2x^2-3x+10x+25=0

We add all the numbers together, and all the variables

-2x^2+7x+25=0

a = -2; b = 7; c = +25;
Δ = b2-4ac
Δ = 72-4·(-2)·25
Δ = 249
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{-(7)-\sqrt{249}}{2*-2}=\frac{-7-\sqrt{249}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{249}}{2*-2}=\frac{-7+\sqrt{249}}{-4}
$