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10x+30x(x-2)=260
We move all terms to the left:
10x+30x(x-2)-(260)=0
We multiply parentheses
30x^2+10x-60x-260=0
We add all the numbers together, and all the variables
30x^2-50x-260=0
a = 30; b = -50; c = -260;
Δ = b2-4ac
Δ = -502-4·30·(-260)
Δ = 33700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33700}=\sqrt{100*337}=\sqrt{100}*\sqrt{337}=10\sqrt{337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{337}}{2*30}=\frac{50-10\sqrt{337}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{337}}{2*30}=\frac{50+10\sqrt{337}}{60} $
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