(x+2)(2x+7)=2x*2x+10x+2

Solution for (x+2)(2x+7)=2x*2x+10x+2 equation:

(x+2)(2x+7)=2x*2x+10x+2

We move all terms to the left:

(x+2)(2x+7)-(2x*2x+10x+2)=0

We add all the numbers together, and all the variables

(x+2)(2x+7)-(10x+2x*2x+2)=0

We get rid of parentheses

(x+2)(2x+7)-10x-2x*2x-2=0

We multiply parentheses ..

(+2x^2+7x+4x+14)-10x-2x*2x-2=0

Wy multiply elements

(+2x^2+7x+4x+14)-4x^2-10x-2=0

We get rid of parentheses

2x^2-4x^2+7x+4x-10x+14-2=0

We add all the numbers together, and all the variables

-2x^2+x+12=0

a = -2; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-2)·12
Δ = 97
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{-(1)-\sqrt{97}}{2*-2}=\frac{-1-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-2}=\frac{-1+\sqrt{97}}{-4}
$