10x^2=2+12x

Solution for 10x^2=2+12x equation:

10x^2=2+12x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

10x^2-12x-2=0

a = 10; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·10·(-2)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{14}}{2*10}=\frac{12-4\sqrt{14}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{14}}{2*10}=\frac{12+4\sqrt{14}}{20}
$