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2x(5x-4)=12
We move all terms to the left:
2x(5x-4)-(12)=0
We multiply parentheses
10x^2-8x-12=0
a = 10; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·10·(-12)
Δ = 544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*10}=\frac{8-4\sqrt{34}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*10}=\frac{8+4\sqrt{34}}{20} $
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