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5(4x-7)(3x-1)2=-5
We move all terms to the left:
5(4x-7)(3x-1)2-(-5)=0
We add all the numbers together, and all the variables
5(4x-7)(3x-1)2+5=0
We multiply parentheses ..
5(+12x^2-4x-21x+7)2+5=0
We multiply parentheses
120x^2-40x-210x+70+5=0
We add all the numbers together, and all the variables
120x^2-250x+75=0
a = 120; b = -250; c = +75;
Δ = b2-4ac
Δ = -2502-4·120·75
Δ = 26500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26500}=\sqrt{100*265}=\sqrt{100}*\sqrt{265}=10\sqrt{265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-10\sqrt{265}}{2*120}=\frac{250-10\sqrt{265}}{240} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+10\sqrt{265}}{2*120}=\frac{250+10\sqrt{265}}{240} $
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