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115=-0.5x^2+25x-160
We move all terms to the left:
115-(-0.5x^2+25x-160)=0
We get rid of parentheses
0.5x^2-25x+160+115=0
We add all the numbers together, and all the variables
0.5x^2-25x+275=0
a = 0.5; b = -25; c = +275;
Δ = b2-4ac
Δ = -252-4·0.5·275
Δ = 75
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{75}=\sqrt{25*3}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{3}}{2*0.5}=\frac{25-5\sqrt{3}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{3}}{2*0.5}=\frac{25+5\sqrt{3}}{1} $
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