x=(2x-5)(x+7)

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

x=(2x-5)(x+7)

We move all terms to the left:

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

We multiply parentheses ..

-((+2x^2+14x-5x-35))+x=0


We calculate terms in parentheses: -((+2x^2+14x-5x-35)), so:

(+2x^2+14x-5x-35)

We get rid of parentheses

2x^2+14x-5x-35

We add all the numbers together, and all the variables

2x^2+9x-35

Back to the equation:

-(2x^2+9x-35)


We add all the numbers together, and all the variables

x-(2x^2+9x-35)=0

We get rid of parentheses

-2x^2+x-9x+35=0

We add all the numbers together, and all the variables

-2x^2-8x+35=0

a = -2; b = -8; c = +35;
Δ = b2-4ac
Δ = -82-4·(-2)·35
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{86}}{2*-2}=\frac{8-2\sqrt{86}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{86}}{2*-2}=\frac{8+2\sqrt{86}}{-4}
$