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(2x-5)(x+3)=7x+21
We move all terms to the left:
(2x-5)(x+3)-(7x+21)=0
We get rid of parentheses
(2x-5)(x+3)-7x-21=0
We multiply parentheses ..
(+2x^2+6x-5x-15)-7x-21=0
We get rid of parentheses
2x^2+6x-5x-7x-15-21=0
We add all the numbers together, and all the variables
2x^2-6x-36=0
a = 2; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·2·(-36)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*2}=\frac{-12}{4} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*2}=\frac{24}{4} =6 $
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