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3(5x+4)5x=-8
We move all terms to the left:
3(5x+4)5x-(-8)=0
We add all the numbers together, and all the variables
3(5x+4)5x+8=0
We multiply parentheses
75x^2+60x+8=0
a = 75; b = 60; c = +8;
Δ = b2-4ac
Δ = 602-4·75·8
Δ = 1200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{3}}{2*75}=\frac{-60-20\sqrt{3}}{150} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{3}}{2*75}=\frac{-60+20\sqrt{3}}{150} $
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