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(2x-22)(5x-8)=180
We move all terms to the left:
(2x-22)(5x-8)-(180)=0
We multiply parentheses ..
(+10x^2-16x-110x+176)-180=0
We get rid of parentheses
10x^2-16x-110x+176-180=0
We add all the numbers together, and all the variables
10x^2-126x-4=0
a = 10; b = -126; c = -4;
Δ = b2-4ac
Δ = -1262-4·10·(-4)
Δ = 16036
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16036}=\sqrt{4*4009}=\sqrt{4}*\sqrt{4009}=2\sqrt{4009}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{4009}}{2*10}=\frac{126-2\sqrt{4009}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{4009}}{2*10}=\frac{126+2\sqrt{4009}}{20} $
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