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(5x+98)(23x-2)=67
We move all terms to the left:
(5x+98)(23x-2)-(67)=0
We multiply parentheses ..
(+115x^2-10x+2254x-196)-67=0
We get rid of parentheses
115x^2-10x+2254x-196-67=0
We add all the numbers together, and all the variables
115x^2+2244x-263=0
a = 115; b = 2244; c = -263;
Δ = b2-4ac
Δ = 22442-4·115·(-263)
Δ = 5156516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5156516}=\sqrt{4*1289129}=\sqrt{4}*\sqrt{1289129}=2\sqrt{1289129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2244)-2\sqrt{1289129}}{2*115}=\frac{-2244-2\sqrt{1289129}}{230} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2244)+2\sqrt{1289129}}{2*115}=\frac{-2244+2\sqrt{1289129}}{230} $
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