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4x(x+10)=48
We move all terms to the left:
4x(x+10)-(48)=0
We multiply parentheses
4x^2+40x-48=0
a = 4; b = 40; c = -48;
Δ = b2-4ac
Δ = 402-4·4·(-48)
Δ = 2368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{37}}{2*4}=\frac{-40-8\sqrt{37}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{37}}{2*4}=\frac{-40+8\sqrt{37}}{8} $
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