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(2x-5)(2x-10)=180
We move all terms to the left:
(2x-5)(2x-10)-(180)=0
We multiply parentheses ..
(+4x^2-20x-10x+50)-180=0
We get rid of parentheses
4x^2-20x-10x+50-180=0
We add all the numbers together, and all the variables
4x^2-30x-130=0
a = 4; b = -30; c = -130;
Δ = b2-4ac
Δ = -302-4·4·(-130)
Δ = 2980
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{745}}{2*4}=\frac{30-2\sqrt{745}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{745}}{2*4}=\frac{30+2\sqrt{745}}{8} $
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