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5x^2+7=13x
We move all terms to the left:
5x^2+7-(13x)=0
a = 5; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·5·7
Δ = 29
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{-(-13)-\sqrt{29}}{2*5}=\frac{13-\sqrt{29}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{29}}{2*5}=\frac{13+\sqrt{29}}{10} $
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