42=7b^2-385

Solution for 42=7b^2-385 equation:

42=7b^2-385

We move all terms to the left:

42-(7b^2-385)=0

We get rid of parentheses

-7b^2+385+42=0

We add all the numbers together, and all the variables

-7b^2+427=0

a = -7; b = 0; c = +427;
Δ = b2-4ac
Δ = 02-4·(-7)·427
Δ = 11956
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:

$\sqrt{\Delta}=\sqrt{11956}=\sqrt{196*61}=\sqrt{196}*\sqrt{61}=14\sqrt{61}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{61}}{2*-7}=\frac{0-14\sqrt{61}}{-14}
=-\frac{14\sqrt{61}}{-14}
=-\frac{\sqrt{61}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{61}}{2*-7}=\frac{0+14\sqrt{61}}{-14}
=\frac{14\sqrt{61}}{-14}
=\frac{\sqrt{61}}{-1}
$