0.75b(8b+4)-1=4b+14

Solution for 0.75b(8b+4)-1=4b+14 equation:

0.75b(8b+4)-1=4b+14

We move all terms to the left:

0.75b(8b+4)-1-(4b+14)=0

We multiply parentheses

0b^2+0b-(4b+14)-1=0

We get rid of parentheses

0b^2+0b-4b-14-1=0

We add all the numbers together, and all the variables

b^2-3b-15=0

a = 1; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·1·(-15)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{69}}{2*1}=\frac{3-\sqrt{69}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*1}=\frac{3+\sqrt{69}}{2}
$