4b-1=(-53b^2)

Solution for 4b-1=(-53b^2) equation:

4b-1=(-53b^2)

We move all terms to the left:

4b-1-((-53b^2))=0


We calculate terms in parentheses: -((-53b^2)), so:

(-53b^2)

We get rid of parentheses

-53b^2

Back to the equation:

-(-53b^2)


We get rid of parentheses

53b^2+4b-1=0

a = 53; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·53·(-1)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{57}}{2*53}=\frac{-4-2\sqrt{57}}{106}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{57}}{2*53}=\frac{-4+2\sqrt{57}}{106}
$