10b^2+5b=4

Solution for 10b^2+5b=4 equation:

10b^2+5b=4

We move all terms to the left:

10b^2+5b-(4)=0

a = 10; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·10·(-4)
Δ = 185
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{-(5)-\sqrt{185}}{2*10}=\frac{-5-\sqrt{185}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{185}}{2*10}=\frac{-5+\sqrt{185}}{20}
$