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(5x-6)(3x+16)=180
We move all terms to the left:
(5x-6)(3x+16)-(180)=0
We multiply parentheses ..
(+15x^2+80x-18x-96)-180=0
We get rid of parentheses
15x^2+80x-18x-96-180=0
We add all the numbers together, and all the variables
15x^2+62x-276=0
a = 15; b = 62; c = -276;
Δ = b2-4ac
Δ = 622-4·15·(-276)
Δ = 20404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20404}=\sqrt{4*5101}=\sqrt{4}*\sqrt{5101}=2\sqrt{5101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{5101}}{2*15}=\frac{-62-2\sqrt{5101}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{5101}}{2*15}=\frac{-62+2\sqrt{5101}}{30} $
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