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(2x+1)(2x-2)=9x+30
We move all terms to the left:
(2x+1)(2x-2)-(9x+30)=0
We get rid of parentheses
(2x+1)(2x-2)-9x-30=0
We multiply parentheses ..
(+4x^2-4x+2x-2)-9x-30=0
We get rid of parentheses
4x^2-4x+2x-9x-2-30=0
We add all the numbers together, and all the variables
4x^2-11x-32=0
a = 4; b = -11; c = -32;
Δ = b2-4ac
Δ = -112-4·4·(-32)
Δ = 633
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{633}}{2*4}=\frac{11-\sqrt{633}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{633}}{2*4}=\frac{11+\sqrt{633}}{8} $
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