-5b^2+7b=-9

Solution for -5b^2+7b=-9 equation:

-5b^2+7b=-9

We move all terms to the left:

-5b^2+7b-(-9)=0

We add all the numbers together, and all the variables

-5b^2+7b+9=0

a = -5; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-5)·9
Δ = 229
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{-(7)-\sqrt{229}}{2*-5}=\frac{-7-\sqrt{229}}{-10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{229}}{2*-5}=\frac{-7+\sqrt{229}}{-10}
$