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8x(5-3x)=-160
We move all terms to the left:
8x(5-3x)-(-160)=0
We add all the numbers together, and all the variables
8x(-3x+5)-(-160)=0
We add all the numbers together, and all the variables
8x(-3x+5)+160=0
We multiply parentheses
-24x^2+40x+160=0
a = -24; b = 40; c = +160;
Δ = b2-4ac
Δ = 402-4·(-24)·160
Δ = 16960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16960}=\sqrt{64*265}=\sqrt{64}*\sqrt{265}=8\sqrt{265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{265}}{2*-24}=\frac{-40-8\sqrt{265}}{-48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{265}}{2*-24}=\frac{-40+8\sqrt{265}}{-48} $
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