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3x-5x(x-5)=-2+5x-8
We move all terms to the left:
3x-5x(x-5)-(-2+5x-8)=0
We add all the numbers together, and all the variables
3x-5x(x-5)-(5x-10)=0
We multiply parentheses
-5x^2+3x+25x-(5x-10)=0
We get rid of parentheses
-5x^2+3x+25x-5x+10=0
We add all the numbers together, and all the variables
-5x^2+23x+10=0
a = -5; b = 23; c = +10;
Δ = b2-4ac
Δ = 232-4·(-5)·10
Δ = 729
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-27}{2*-5}=\frac{-50}{-10} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+27}{2*-5}=\frac{4}{-10} =-2/5 $
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