2x^2+14x+102=4x^2+4x+1

Solution for 2x^2+14x+102=4x^2+4x+1 equation:

2x^2+14x+102=4x^2+4x+1

We move all terms to the left:

2x^2+14x+102-(4x^2+4x+1)=0

We get rid of parentheses

2x^2-4x^2+14x-4x-1+102=0

We add all the numbers together, and all the variables

-2x^2+10x+101=0

a = -2; b = 10; c = +101;
Δ = b2-4ac
Δ = 102-4·(-2)·101
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{227}}{2*-2}=\frac{-10-2\sqrt{227}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{227}}{2*-2}=\frac{-10+2\sqrt{227}}{-4}
$