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6(5x-12)10x=8
We move all terms to the left:
6(5x-12)10x-(8)=0
We multiply parentheses
300x^2-720x-8=0
a = 300; b = -720; c = -8;
Δ = b2-4ac
Δ = -7202-4·300·(-8)
Δ = 528000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{528000}=\sqrt{1600*330}=\sqrt{1600}*\sqrt{330}=40\sqrt{330}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-40\sqrt{330}}{2*300}=\frac{720-40\sqrt{330}}{600} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+40\sqrt{330}}{2*300}=\frac{720+40\sqrt{330}}{600} $
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