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(5x-16)(3x-2)=180
We move all terms to the left:
(5x-16)(3x-2)-(180)=0
We multiply parentheses ..
(+15x^2-10x-48x+32)-180=0
We get rid of parentheses
15x^2-10x-48x+32-180=0
We add all the numbers together, and all the variables
15x^2-58x-148=0
a = 15; b = -58; c = -148;
Δ = b2-4ac
Δ = -582-4·15·(-148)
Δ = 12244
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12244}=\sqrt{4*3061}=\sqrt{4}*\sqrt{3061}=2\sqrt{3061}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{3061}}{2*15}=\frac{58-2\sqrt{3061}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{3061}}{2*15}=\frac{58+2\sqrt{3061}}{30} $
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