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5x(2x-3)=16
We move all terms to the left:
5x(2x-3)-(16)=0
We multiply parentheses
10x^2-15x-16=0
a = 10; b = -15; c = -16;
Δ = b2-4ac
Δ = -152-4·10·(-16)
Δ = 865
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{865}}{2*10}=\frac{15-\sqrt{865}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{865}}{2*10}=\frac{15+\sqrt{865}}{20} $
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