7b^2=3b+10

Solution for 7b^2=3b+10 equation:

7b^2=3b+10

We move all terms to the left:

7b^2-(3b+10)=0

We get rid of parentheses

7b^2-3b-10=0

a = 7; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·7·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*7}=\frac{-14}{14}
=-1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*7}=\frac{20}{14}
=1+3/7
$