7b^2+4=627

Solution for 7b^2+4=627 equation:

7b^2+4=627

We move all terms to the left:

7b^2+4-(627)=0

We add all the numbers together, and all the variables

7b^2-623=0

a = 7; b = 0; c = -623;
Δ = b2-4ac
Δ = 02-4·7·(-623)
Δ = 17444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17444}=\sqrt{196*89}=\sqrt{196}*\sqrt{89}=14\sqrt{89}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{89}}{2*7}=\frac{0-14\sqrt{89}}{14}
=-\frac{14\sqrt{89}}{14}
=-\sqrt{89}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{89}}{2*7}=\frac{0+14\sqrt{89}}{14}
=\frac{14\sqrt{89}}{14}
=\sqrt{89}
$