(2b^2/2)-1.5b-52=0

Solution for (2b^2/2)-1.5b-52=0 equation:

(2b^2/2)-1.5b-52=0

We add all the numbers together, and all the variables

-1.5b+(2b^2/2)-52=0

We get rid of parentheses

2b^2/2-1.5b-52=0

We multiply all the terms by the denominator


2b^2-(1.5b)*2-52*2=0

We add all the numbers together, and all the variables

2b^2-(+1.5b)*2-52*2=0

We add all the numbers together, and all the variables

2b^2-(+1.5b)*2-104=0

We multiply parentheses

2b^2-2b-104=0

a = 2; b = -2; c = -104;
Δ = b2-4ac
Δ = -22-4·2·(-104)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{209}}{2*2}=\frac{2-2\sqrt{209}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{209}}{2*2}=\frac{2+2\sqrt{209}}{4}
$