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5x(2-x)=3x-14
We move all terms to the left:
5x(2-x)-(3x-14)=0
We add all the numbers together, and all the variables
5x(-1x+2)-(3x-14)=0
We multiply parentheses
-5x^2+10x-(3x-14)=0
We get rid of parentheses
-5x^2+10x-3x+14=0
We add all the numbers together, and all the variables
-5x^2+7x+14=0
a = -5; b = 7; c = +14;
Δ = b2-4ac
Δ = 72-4·(-5)·14
Δ = 329
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{329}}{2*-5}=\frac{-7-\sqrt{329}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{329}}{2*-5}=\frac{-7+\sqrt{329}}{-10} $
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