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(2x+5)(7-3x)-9=0
We add all the numbers together, and all the variables
(2x+5)(-3x+7)-9=0
We multiply parentheses ..
(-6x^2+14x-15x+35)-9=0
We get rid of parentheses
-6x^2+14x-15x+35-9=0
We add all the numbers together, and all the variables
-6x^2-1x+26=0
a = -6; b = -1; c = +26;
Δ = b2-4ac
Δ = -12-4·(-6)·26
Δ = 625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*-6}=\frac{-24}{-12} =+2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*-6}=\frac{26}{-12} =-2+1/6 $
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