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(6x-8)(5x-14)=180
We move all terms to the left:
(6x-8)(5x-14)-(180)=0
We multiply parentheses ..
(+30x^2-84x-40x+112)-180=0
We get rid of parentheses
30x^2-84x-40x+112-180=0
We add all the numbers together, and all the variables
30x^2-124x-68=0
a = 30; b = -124; c = -68;
Δ = b2-4ac
Δ = -1242-4·30·(-68)
Δ = 23536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23536}=\sqrt{16*1471}=\sqrt{16}*\sqrt{1471}=4\sqrt{1471}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-4\sqrt{1471}}{2*30}=\frac{124-4\sqrt{1471}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+4\sqrt{1471}}{2*30}=\frac{124+4\sqrt{1471}}{60} $
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