4x2+10x+4=12

Solution for 4x2+10x+4=12 equation:

4x^2+10x+4=12

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2+10x-8=0

a = 4; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·4·(-8)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{57}}{2*4}=\frac{-10-2\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{57}}{2*4}=\frac{-10+2\sqrt{57}}{8}
$