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(5x-10)(3x)=40
We move all terms to the left:
(5x-10)(3x)-(40)=0
We multiply parentheses
15x^2-30x-40=0
a = 15; b = -30; c = -40;
Δ = b2-4ac
Δ = -302-4·15·(-40)
Δ = 3300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{33}}{2*15}=\frac{30-10\sqrt{33}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{33}}{2*15}=\frac{30+10\sqrt{33}}{30} $
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