5x^2+2x+10=16x^2+8x+1

Solution for 5x^2+2x+10=16x^2+8x+1 equation:

5x^2+2x+10=16x^2+8x+1

We move all terms to the left:

5x^2+2x+10-(16x^2+8x+1)=0

We get rid of parentheses

5x^2-16x^2+2x-8x-1+10=0

We add all the numbers together, and all the variables

-11x^2-6x+9=0

a = -11; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-11)·9
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{3}}{2*-11}=\frac{6-12\sqrt{3}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{3}}{2*-11}=\frac{6+12\sqrt{3}}{-22}
$