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5x(3x+4)=180
We move all terms to the left:
5x(3x+4)-(180)=0
We multiply parentheses
15x^2+20x-180=0
a = 15; b = 20; c = -180;
Δ = b2-4ac
Δ = 202-4·15·(-180)
Δ = 11200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-40\sqrt{7}}{2*15}=\frac{-20-40\sqrt{7}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+40\sqrt{7}}{2*15}=\frac{-20+40\sqrt{7}}{30} $
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