10-4x=4x^2+12x+9

Solution for 10-4x=4x^2+12x+9 equation:

10-4x=4x^2+12x+9

We move all terms to the left:

10-4x-(4x^2+12x+9)=0

We get rid of parentheses

-4x^2-4x-12x-9+10=0

We add all the numbers together, and all the variables

-4x^2-16x+1=0

a = -4; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-4)·1
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{17}}{2*-4}=\frac{16-4\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*-4}=\frac{16+4\sqrt{17}}{-8}
$