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-5(2x+6)9x=-32
We move all terms to the left:
-5(2x+6)9x-(-32)=0
We add all the numbers together, and all the variables
-5(2x+6)9x+32=0
We multiply parentheses
-90x^2-270x+32=0
a = -90; b = -270; c = +32;
Δ = b2-4ac
Δ = -2702-4·(-90)·32
Δ = 84420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84420}=\sqrt{36*2345}=\sqrt{36}*\sqrt{2345}=6\sqrt{2345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-6\sqrt{2345}}{2*-90}=\frac{270-6\sqrt{2345}}{-180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+6\sqrt{2345}}{2*-90}=\frac{270+6\sqrt{2345}}{-180} $
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