8X2+4x+7=12

Solution for 8X2+4x+7=12 equation:

8X^2+4X+7=12

We move all terms to the left:

8X^2+4X+7-(12)=0

We add all the numbers together, and all the variables

8X^2+4X-5=0

a = 8; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·8·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*8}=\frac{-4-4\sqrt{11}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*8}=\frac{-4+4\sqrt{11}}{16}
$