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3x-5x(x-3)=-8+3x-17
We move all terms to the left:
3x-5x(x-3)-(-8+3x-17)=0
We add all the numbers together, and all the variables
3x-5x(x-3)-(3x-25)=0
We multiply parentheses
-5x^2+3x+15x-(3x-25)=0
We get rid of parentheses
-5x^2+3x+15x-3x+25=0
We add all the numbers together, and all the variables
-5x^2+15x+25=0
a = -5; b = 15; c = +25;
Δ = b2-4ac
Δ = 152-4·(-5)·25
Δ = 725
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{29}}{2*-5}=\frac{-15-5\sqrt{29}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{29}}{2*-5}=\frac{-15+5\sqrt{29}}{-10} $
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