0=7(x+2,5)(x-17)

Solution for 0=7(x+2,5)(x-17) equation:

0=7(x+2.5)(x-17)

We move all terms to the left:

0-(7(x+2.5)(x-17))=0

We add all the numbers together, and all the variables

-(7(x+2.5)(x-17))=0

We multiply parentheses ..

-(7(+x^2-17x+2.5x-42.5))=0


We calculate terms in parentheses: -(7(+x^2-17x+2.5x-42.5)), so:

7(+x^2-17x+2.5x-42.5)

We multiply parentheses

7x^2-119x+14x-297.5

We add all the numbers together, and all the variables

7x^2-105x-297.5

Back to the equation:

-(7x^2-105x-297.5)


We get rid of parentheses

-7x^2+105x+297.5=0

a = -7; b = 105; c = +297.5;
Δ = b2-4ac
Δ = 1052-4·(-7)·297.5
Δ = 19355
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:

$\sqrt{\Delta}=\sqrt{19355}=\sqrt{49*395}=\sqrt{49}*\sqrt{395}=7\sqrt{395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-7\sqrt{395}}{2*-7}=\frac{-105-7\sqrt{395}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+7\sqrt{395}}{2*-7}=\frac{-105+7\sqrt{395}}{-14}
$