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2x(6x-1)+2(2x+5)=120
We move all terms to the left:
2x(6x-1)+2(2x+5)-(120)=0
We multiply parentheses
12x^2-2x+4x+10-120=0
We add all the numbers together, and all the variables
12x^2+2x-110=0
a = 12; b = 2; c = -110;
Δ = b2-4ac
Δ = 22-4·12·(-110)
Δ = 5284
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5284}=\sqrt{4*1321}=\sqrt{4}*\sqrt{1321}=2\sqrt{1321}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1321}}{2*12}=\frac{-2-2\sqrt{1321}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1321}}{2*12}=\frac{-2+2\sqrt{1321}}{24} $
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