40x+8(x)(1.5x)=572

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Solution for 40x+8(x)(1.5x)=572 equation:



40x+8(x)(1.5x)=572
We move all terms to the left:
40x+8(x)(1.5x)-(572)=0
We add all the numbers together, and all the variables
40x+8x(+1.5x)-572=0
We multiply parentheses
8x^2+40x-572=0
a = 8; b = 40; c = -572;
Δ = b2-4ac
Δ = 402-4·8·(-572)
Δ = 19904
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:
$\sqrt{\Delta}=\sqrt{19904}=\sqrt{64*311}=\sqrt{64}*\sqrt{311}=8\sqrt{311}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{311}}{2*8}=\frac{-40-8\sqrt{311}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{311}}{2*8}=\frac{-40+8\sqrt{311}}{16} $

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