-7-4b2=-45

Solution for -7-4b2=-45 equation:

-7-4b^2=-45

We move all terms to the left:

-7-4b^2-(-45)=0

We add all the numbers together, and all the variables

-4b^2+38=0

a = -4; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-4)·38
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{38}}{2*-4}=\frac{0-4\sqrt{38}}{-8}
=-\frac{4\sqrt{38}}{-8}
=-\frac{\sqrt{38}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{38}}{2*-4}=\frac{0+4\sqrt{38}}{-8}
=\frac{4\sqrt{38}}{-8}
=\frac{\sqrt{38}}{-2}
$