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9(2x-3)5x+17=-7x
We move all terms to the left:
9(2x-3)5x+17-(-7x)=0
We multiply parentheses
90x^2-135x-(-7x)+17=0
We get rid of parentheses
90x^2-135x+7x+17=0
We add all the numbers together, and all the variables
90x^2-128x+17=0
a = 90; b = -128; c = +17;
Δ = b2-4ac
Δ = -1282-4·90·17
Δ = 10264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10264}=\sqrt{4*2566}=\sqrt{4}*\sqrt{2566}=2\sqrt{2566}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-2\sqrt{2566}}{2*90}=\frac{128-2\sqrt{2566}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+2\sqrt{2566}}{2*90}=\frac{128+2\sqrt{2566}}{180} $
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