-4.9x^2+28x+37=7

Solution for -4.9x^2+28x+37=7 equation:

-4.9x^2+28x+37=7

We move all terms to the left:

-4.9x^2+28x+37-(7)=0

We add all the numbers together, and all the variables

-4.9x^2+28x+30=0

a = -4.9; b = 28; c = +30;
Δ = b2-4ac
Δ = 282-4·(-4.9)·30
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-14\sqrt{7}}{2*-4.9}=\frac{-28-14\sqrt{7}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14\sqrt{7}}{2*-4.9}=\frac{-28+14\sqrt{7}}{-9.8}
$