49x2+28x=22

Solution for 49x2+28x=22 equation:

49x^2+28x=22

We move all terms to the left:

49x^2+28x-(22)=0

a = 49; b = 28; c = -22;
Δ = b2-4ac
Δ = 282-4·49·(-22)
Δ = 5096
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:

$\sqrt{\Delta}=\sqrt{5096}=\sqrt{196*26}=\sqrt{196}*\sqrt{26}=14\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-14\sqrt{26}}{2*49}=\frac{-28-14\sqrt{26}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14\sqrt{26}}{2*49}=\frac{-28+14\sqrt{26}}{98}
$