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5x^2=115-5x
We move all terms to the left:
5x^2-(115-5x)=0
We add all the numbers together, and all the variables
5x^2-(-5x+115)=0
We get rid of parentheses
5x^2+5x-115=0
a = 5; b = 5; c = -115;
Δ = b2-4ac
Δ = 52-4·5·(-115)
Δ = 2325
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2325}=\sqrt{25*93}=\sqrt{25}*\sqrt{93}=5\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{93}}{2*5}=\frac{-5-5\sqrt{93}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{93}}{2*5}=\frac{-5+5\sqrt{93}}{10} $
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