2b^2=102-5b

Solution for 2b^2=102-5b equation:

2b^2=102-5b

We move all terms to the left:

2b^2-(102-5b)=0

We add all the numbers together, and all the variables

2b^2-(-5b+102)=0

We get rid of parentheses

2b^2+5b-102=0

a = 2; b = 5; c = -102;
Δ = b2-4ac
Δ = 52-4·2·(-102)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*2}=\frac{-34}{4}
=-8+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*2}=\frac{24}{4}
=6
$