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(2x-4)+(5x-13)(x+9)=189
We move all terms to the left:
(2x-4)+(5x-13)(x+9)-(189)=0
We get rid of parentheses
2x+(5x-13)(x+9)-4-189=0
We multiply parentheses ..
(+5x^2+45x-13x-117)+2x-4-189=0
We add all the numbers together, and all the variables
(+5x^2+45x-13x-117)+2x-193=0
We get rid of parentheses
5x^2+45x-13x+2x-117-193=0
We add all the numbers together, and all the variables
5x^2+34x-310=0
a = 5; b = 34; c = -310;
Δ = b2-4ac
Δ = 342-4·5·(-310)
Δ = 7356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7356}=\sqrt{4*1839}=\sqrt{4}*\sqrt{1839}=2\sqrt{1839}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{1839}}{2*5}=\frac{-34-2\sqrt{1839}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{1839}}{2*5}=\frac{-34+2\sqrt{1839}}{10} $
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