(x+7)(x-2)=(3x-1)(2x+14)

Solution for (x+7)(x-2)=(3x-1)(2x+14) equation:

(x+7)(x-2)=(3x-1)(2x+14)

We move all terms to the left:

(x+7)(x-2)-((3x-1)(2x+14))=0

We multiply parentheses ..

(+x^2-2x+7x-14)-((3x-1)(2x+14))=0


We calculate terms in parentheses: -((3x-1)(2x+14)), so:

(3x-1)(2x+14)

We multiply parentheses ..

(+6x^2+42x-2x-14)

We get rid of parentheses

6x^2+42x-2x-14

We add all the numbers together, and all the variables

6x^2+40x-14

Back to the equation:

-(6x^2+40x-14)


We get rid of parentheses

x^2-6x^2-2x+7x-40x-14+14=0

We add all the numbers together, and all the variables

-5x^2-35x=0

a = -5; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-5)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-5}=\frac{70}{-10}
=-7
$