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(2x-5)(6x-1)=120
We move all terms to the left:
(2x-5)(6x-1)-(120)=0
We multiply parentheses ..
(+12x^2-2x-30x+5)-120=0
We get rid of parentheses
12x^2-2x-30x+5-120=0
We add all the numbers together, and all the variables
12x^2-32x-115=0
a = 12; b = -32; c = -115;
Δ = b2-4ac
Δ = -322-4·12·(-115)
Δ = 6544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{409}}{2*12}=\frac{32-4\sqrt{409}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{409}}{2*12}=\frac{32+4\sqrt{409}}{24} $
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