10b^2-9=6b

Solution for 10b^2-9=6b equation:

10b^2-9=6b

We move all terms to the left:

10b^2-9-(6b)=0

a = 10; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·10·(-9)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{11}}{2*10}=\frac{6-6\sqrt{11}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{11}}{2*10}=\frac{6+6\sqrt{11}}{20}
$