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5x^2+35x=0.5
We move all terms to the left:
5x^2+35x-(0.5)=0
We add all the numbers together, and all the variables
5x^2+35x-0.5=0
a = 5; b = 35; c = -0.5;
Δ = b2-4ac
Δ = 352-4·5·(-0.5)
Δ = 1235
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1235}}{2*5}=\frac{-35-\sqrt{1235}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1235}}{2*5}=\frac{-35+\sqrt{1235}}{10} $
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