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(7x-1)(6x-3)=180
We move all terms to the left:
(7x-1)(6x-3)-(180)=0
We multiply parentheses ..
(+42x^2-21x-6x+3)-180=0
We get rid of parentheses
42x^2-21x-6x+3-180=0
We add all the numbers together, and all the variables
42x^2-27x-177=0
a = 42; b = -27; c = -177;
Δ = b2-4ac
Δ = -272-4·42·(-177)
Δ = 30465
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30465}=\sqrt{9*3385}=\sqrt{9}*\sqrt{3385}=3\sqrt{3385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{3385}}{2*42}=\frac{27-3\sqrt{3385}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{3385}}{2*42}=\frac{27+3\sqrt{3385}}{84} $
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