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(x-15)(x+3)=90
We move all terms to the left:
(x-15)(x+3)-(90)=0
We multiply parentheses ..
(+x^2+3x-15x-45)-90=0
We get rid of parentheses
x^2+3x-15x-45-90=0
We add all the numbers together, and all the variables
x^2-12x-135=0
a = 1; b = -12; c = -135;
Δ = b2-4ac
Δ = -122-4·1·(-135)
Δ = 684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{19}}{2*1}=\frac{12-6\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{19}}{2*1}=\frac{12+6\sqrt{19}}{2} $
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