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(2x-1)(x+5)=38
We move all terms to the left:
(2x-1)(x+5)-(38)=0
We multiply parentheses ..
(+2x^2+10x-1x-5)-38=0
We get rid of parentheses
2x^2+10x-1x-5-38=0
We add all the numbers together, and all the variables
2x^2+9x-43=0
a = 2; b = 9; c = -43;
Δ = b2-4ac
Δ = 92-4·2·(-43)
Δ = 425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5\sqrt{17}}{2*2}=\frac{-9-5\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5\sqrt{17}}{2*2}=\frac{-9+5\sqrt{17}}{4} $
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