49x^2-4x=15

Solution for 49x^2-4x=15 equation:

49x^2-4x=15

We move all terms to the left:

49x^2-4x-(15)=0

a = 49; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·49·(-15)
Δ = 2956
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:

$\sqrt{\Delta}=\sqrt{2956}=\sqrt{4*739}=\sqrt{4}*\sqrt{739}=2\sqrt{739}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{739}}{2*49}=\frac{4-2\sqrt{739}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{739}}{2*49}=\frac{4+2\sqrt{739}}{98}
$