49x^2+14x=12

Solution for 49x^2+14x=12 equation:

49x^2+14x=12

We move all terms to the left:

49x^2+14x-(12)=0

a = 49; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·49·(-12)
Δ = 2548
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:

$\sqrt{\Delta}=\sqrt{2548}=\sqrt{196*13}=\sqrt{196}*\sqrt{13}=14\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{13}}{2*49}=\frac{-14-14\sqrt{13}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{13}}{2*49}=\frac{-14+14\sqrt{13}}{98}
$