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(2x-3)(x+4)=90
We move all terms to the left:
(2x-3)(x+4)-(90)=0
We multiply parentheses ..
(+2x^2+8x-3x-12)-90=0
We get rid of parentheses
2x^2+8x-3x-12-90=0
We add all the numbers together, and all the variables
2x^2+5x-102=0
a = 2; b = 5; c = -102;
Δ = b2-4ac
Δ = 52-4·2·(-102)
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*2}=\frac{-34}{4} =-8+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*2}=\frac{24}{4} =6 $
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