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(x-23)(2x+29)=90
We move all terms to the left:
(x-23)(2x+29)-(90)=0
We multiply parentheses ..
(+2x^2+29x-46x-667)-90=0
We get rid of parentheses
2x^2+29x-46x-667-90=0
We add all the numbers together, and all the variables
2x^2-17x-757=0
a = 2; b = -17; c = -757;
Δ = b2-4ac
Δ = -172-4·2·(-757)
Δ = 6345
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6345}=\sqrt{9*705}=\sqrt{9}*\sqrt{705}=3\sqrt{705}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{705}}{2*2}=\frac{17-3\sqrt{705}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{705}}{2*2}=\frac{17+3\sqrt{705}}{4} $
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