5b^2+14b+13=10

Solution for 5b^2+14b+13=10 equation:

5b^2+14b+13=10

We move all terms to the left:

5b^2+14b+13-(10)=0

We add all the numbers together, and all the variables

5b^2+14b+3=0

a = 5; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·5·3
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{34}}{2*5}=\frac{-14-2\sqrt{34}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{34}}{2*5}=\frac{-14+2\sqrt{34}}{10}
$