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4x(5x+5)=103
We move all terms to the left:
4x(5x+5)-(103)=0
We multiply parentheses
20x^2+20x-103=0
a = 20; b = 20; c = -103;
Δ = b2-4ac
Δ = 202-4·20·(-103)
Δ = 8640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-24\sqrt{15}}{2*20}=\frac{-20-24\sqrt{15}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+24\sqrt{15}}{2*20}=\frac{-20+24\sqrt{15}}{40} $
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