3x+7x+1=2x(5x+1)+2

Solution for 3x+7x+1=2x(5x+1)+2 equation:

3x+7x+1=2x(5x+1)+2

We move all terms to the left:

3x+7x+1-(2x(5x+1)+2)=0

We add all the numbers together, and all the variables

10x-(2x(5x+1)+2)+1=0


We calculate terms in parentheses: -(2x(5x+1)+2), so:

2x(5x+1)+2

We multiply parentheses

10x^2+2x+2

Back to the equation:

-(10x^2+2x+2)


We get rid of parentheses

-10x^2+10x-2x-2+1=0

We add all the numbers together, and all the variables

-10x^2+8x-1=0

a = -10; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-10)·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{6}}{2*-10}=\frac{-8-2\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*-10}=\frac{-8+2\sqrt{6}}{-20}
$