12x^2=10x+1

Solution for 12x^2=10x+1 equation:

12x^2=10x+1

We move all terms to the left:

12x^2-(10x+1)=0

We get rid of parentheses

12x^2-10x-1=0

a = 12; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·12·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*12}=\frac{10-2\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*12}=\frac{10+2\sqrt{37}}{24}
$