3x+7x+1=10x2+2

Solution for 3x+7x+1=10x2+2 equation:

3x+7x+1=10x^2+2

We move all terms to the left:

3x+7x+1-(10x^2+2)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -10; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-10)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*-10}=\frac{-10-2\sqrt{15}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*-10}=\frac{-10+2\sqrt{15}}{-20}
$