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(2x-13)(4x-5)=180
We move all terms to the left:
(2x-13)(4x-5)-(180)=0
We multiply parentheses ..
(+8x^2-10x-52x+65)-180=0
We get rid of parentheses
8x^2-10x-52x+65-180=0
We add all the numbers together, and all the variables
8x^2-62x-115=0
a = 8; b = -62; c = -115;
Δ = b2-4ac
Δ = -622-4·8·(-115)
Δ = 7524
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7524}=\sqrt{36*209}=\sqrt{36}*\sqrt{209}=6\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-6\sqrt{209}}{2*8}=\frac{62-6\sqrt{209}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+6\sqrt{209}}{2*8}=\frac{62+6\sqrt{209}}{16} $
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