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5x(5x-2)=40
We move all terms to the left:
5x(5x-2)-(40)=0
We multiply parentheses
25x^2-10x-40=0
a = 25; b = -10; c = -40;
Δ = b2-4ac
Δ = -102-4·25·(-40)
Δ = 4100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{41}}{2*25}=\frac{10-10\sqrt{41}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{41}}{2*25}=\frac{10+10\sqrt{41}}{50} $
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