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3x-5x(x-5)=-8+4x-9
We move all terms to the left:
3x-5x(x-5)-(-8+4x-9)=0
We add all the numbers together, and all the variables
3x-5x(x-5)-(4x-17)=0
We multiply parentheses
-5x^2+3x+25x-(4x-17)=0
We get rid of parentheses
-5x^2+3x+25x-4x+17=0
We add all the numbers together, and all the variables
-5x^2+24x+17=0
a = -5; b = 24; c = +17;
Δ = b2-4ac
Δ = 242-4·(-5)·17
Δ = 916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{229}}{2*-5}=\frac{-24-2\sqrt{229}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{229}}{2*-5}=\frac{-24+2\sqrt{229}}{-10} $
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