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5x-3x(x-5)=-8+5x-1
We move all terms to the left:
5x-3x(x-5)-(-8+5x-1)=0
We add all the numbers together, and all the variables
5x-3x(x-5)-(5x-9)=0
We multiply parentheses
-3x^2+5x+15x-(5x-9)=0
We get rid of parentheses
-3x^2+5x+15x-5x+9=0
We add all the numbers together, and all the variables
-3x^2+15x+9=0
a = -3; b = 15; c = +9;
Δ = b2-4ac
Δ = 152-4·(-3)·9
Δ = 333
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{37}}{2*-3}=\frac{-15-3\sqrt{37}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{37}}{2*-3}=\frac{-15+3\sqrt{37}}{-6} $
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