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5x(2x+2)=12
We move all terms to the left:
5x(2x+2)-(12)=0
We multiply parentheses
10x^2+10x-12=0
a = 10; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·10·(-12)
Δ = 580
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{145}}{2*10}=\frac{-10-2\sqrt{145}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{145}}{2*10}=\frac{-10+2\sqrt{145}}{20} $
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