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(2x+14)-(2x+5)(3x-2)=0
We get rid of parentheses
2x-(2x+5)(3x-2)+14=0
We multiply parentheses ..
-(+6x^2-4x+15x-10)+2x+14=0
We get rid of parentheses
-6x^2+4x-15x+2x+10+14=0
We add all the numbers together, and all the variables
-6x^2-9x+24=0
a = -6; b = -9; c = +24;
Δ = b2-4ac
Δ = -92-4·(-6)·24
Δ = 657
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{73}}{2*-6}=\frac{9-3\sqrt{73}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{73}}{2*-6}=\frac{9+3\sqrt{73}}{-12} $
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