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-5x^2+3x=-5
We move all terms to the left:
-5x^2+3x-(-5)=0
We add all the numbers together, and all the variables
-5x^2+3x+5=0
a = -5; b = 3; c = +5;
Δ = b2-4ac
Δ = 32-4·(-5)·5
Δ = 109
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{-(3)-\sqrt{109}}{2*-5}=\frac{-3-\sqrt{109}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{109}}{2*-5}=\frac{-3+\sqrt{109}}{-10} $
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