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5x-3x(x-4)=-8+5x+14
We move all terms to the left:
5x-3x(x-4)-(-8+5x+14)=0
We add all the numbers together, and all the variables
5x-3x(x-4)-(5x+6)=0
We multiply parentheses
-3x^2+5x+12x-(5x+6)=0
We get rid of parentheses
-3x^2+5x+12x-5x-6=0
We add all the numbers together, and all the variables
-3x^2+12x-6=0
a = -3; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·(-3)·(-6)
Δ = 72
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*-3}=\frac{-12-6\sqrt{2}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*-3}=\frac{-12+6\sqrt{2}}{-6} $
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