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(5y-4)(3y+14)=180
We move all terms to the left:
(5y-4)(3y+14)-(180)=0
We multiply parentheses ..
(+15y^2+70y-12y-56)-180=0
We get rid of parentheses
15y^2+70y-12y-56-180=0
We add all the numbers together, and all the variables
15y^2+58y-236=0
a = 15; b = 58; c = -236;
Δ = b2-4ac
Δ = 582-4·15·(-236)
Δ = 17524
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17524}=\sqrt{4*4381}=\sqrt{4}*\sqrt{4381}=2\sqrt{4381}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{4381}}{2*15}=\frac{-58-2\sqrt{4381}}{30} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{4381}}{2*15}=\frac{-58+2\sqrt{4381}}{30} $
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