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14(2x-3)60x=5(15-9)
We move all terms to the left:
14(2x-3)60x-(5(15-9))=0
We add all the numbers together, and all the variables
14(2x-3)60x-(56)=0
We add all the numbers together, and all the variables
14(2x-3)60x-56=0
We multiply parentheses
1680x^2-2520x-56=0
a = 1680; b = -2520; c = -56;
Δ = b2-4ac
Δ = -25202-4·1680·(-56)
Δ = 6726720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6726720}=\sqrt{3136*2145}=\sqrt{3136}*\sqrt{2145}=56\sqrt{2145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2520)-56\sqrt{2145}}{2*1680}=\frac{2520-56\sqrt{2145}}{3360} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2520)+56\sqrt{2145}}{2*1680}=\frac{2520+56\sqrt{2145}}{3360} $
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