6+5b(b=14)

Solution for 6+5b(b=14) equation:

6+5b(b=14)

We move all terms to the left:

6+5b(b-(14))=0

We multiply parentheses

5b^2-70b+6=0

a = 5; b = -70; c = +6;
Δ = b2-4ac
Δ = -702-4·5·6
Δ = 4780
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:

$\sqrt{\Delta}=\sqrt{4780}=\sqrt{4*1195}=\sqrt{4}*\sqrt{1195}=2\sqrt{1195}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1195}}{2*5}=\frac{70-2\sqrt{1195}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1195}}{2*5}=\frac{70+2\sqrt{1195}}{10}
$