(x+7)(2x-1)=(2x+1)(2-5)

Solution for (x+7)(2x-1)=(2x+1)(2-5) equation:

(x+7)(2x-1)=(2x+1)(2-5)

We move all terms to the left:

(x+7)(2x-1)-((2x+1)(2-5))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

(2x+1)(-3)

We multiply parentheses ..

(-6x-3)

We get rid of parentheses

-6x-3

Back to the equation:

-(-6x-3)


We get rid of parentheses

2x^2-1x+14x+6x-7+3=0

We add all the numbers together, and all the variables

2x^2+19x-4=0

a = 2; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·2·(-4)
Δ = 393
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{-(19)-\sqrt{393}}{2*2}=\frac{-19-\sqrt{393}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{393}}{2*2}=\frac{-19+\sqrt{393}}{4}
$