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(2x+5)(6x-1)-5=120
We move all terms to the left:
(2x+5)(6x-1)-5-(120)=0
We add all the numbers together, and all the variables
(2x+5)(6x-1)-125=0
We multiply parentheses ..
(+12x^2-2x+30x-5)-125=0
We get rid of parentheses
12x^2-2x+30x-5-125=0
We add all the numbers together, and all the variables
12x^2+28x-130=0
a = 12; b = 28; c = -130;
Δ = b2-4ac
Δ = 282-4·12·(-130)
Δ = 7024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7024}=\sqrt{16*439}=\sqrt{16}*\sqrt{439}=4\sqrt{439}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{439}}{2*12}=\frac{-28-4\sqrt{439}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{439}}{2*12}=\frac{-28+4\sqrt{439}}{24} $
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