-0.5x^2+25x+66=109

Solution for -0.5x^2+25x+66=109 equation:

-0.5x^2+25x+66=109

We move all terms to the left:

-0.5x^2+25x+66-(109)=0

We add all the numbers together, and all the variables

-0.5x^2+25x-43=0

a = -0.5; b = 25; c = -43;
Δ = b2-4ac
Δ = 252-4·(-0.5)·(-43)
Δ = 539
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{539}=\sqrt{49*11}=\sqrt{49}*\sqrt{11}=7\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7\sqrt{11}}{2*-0.5}=\frac{-25-7\sqrt{11}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7\sqrt{11}}{2*-0.5}=\frac{-25+7\sqrt{11}}{-1}
$