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(10x-14)(7x-8)=180
We move all terms to the left:
(10x-14)(7x-8)-(180)=0
We multiply parentheses ..
(+70x^2-80x-98x+112)-180=0
We get rid of parentheses
70x^2-80x-98x+112-180=0
We add all the numbers together, and all the variables
70x^2-178x-68=0
a = 70; b = -178; c = -68;
Δ = b2-4ac
Δ = -1782-4·70·(-68)
Δ = 50724
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{50724}=\sqrt{36*1409}=\sqrt{36}*\sqrt{1409}=6\sqrt{1409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-6\sqrt{1409}}{2*70}=\frac{178-6\sqrt{1409}}{140} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+6\sqrt{1409}}{2*70}=\frac{178+6\sqrt{1409}}{140} $
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