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-5x^2+7x=-1
We move all terms to the left:
-5x^2+7x-(-1)=0
We add all the numbers together, and all the variables
-5x^2+7x+1=0
a = -5; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-5)·1
Δ = 69
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{-(7)-\sqrt{69}}{2*-5}=\frac{-7-\sqrt{69}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*-5}=\frac{-7+\sqrt{69}}{-10} $
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