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(7x-30)(6x-10)=180
We move all terms to the left:
(7x-30)(6x-10)-(180)=0
We multiply parentheses ..
(+42x^2-70x-180x+300)-180=0
We get rid of parentheses
42x^2-70x-180x+300-180=0
We add all the numbers together, and all the variables
42x^2-250x+120=0
a = 42; b = -250; c = +120;
Δ = b2-4ac
Δ = -2502-4·42·120
Δ = 42340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{42340}=\sqrt{4*10585}=\sqrt{4}*\sqrt{10585}=2\sqrt{10585}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{10585}}{2*42}=\frac{250-2\sqrt{10585}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{10585}}{2*42}=\frac{250+2\sqrt{10585}}{84} $
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