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6x^2-23x=18+35x
We move all terms to the left:
6x^2-23x-(18+35x)=0
We add all the numbers together, and all the variables
6x^2-23x-(35x+18)=0
We get rid of parentheses
6x^2-23x-35x-18=0
We add all the numbers together, and all the variables
6x^2-58x-18=0
a = 6; b = -58; c = -18;
Δ = b2-4ac
Δ = -582-4·6·(-18)
Δ = 3796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3796}=\sqrt{4*949}=\sqrt{4}*\sqrt{949}=2\sqrt{949}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{949}}{2*6}=\frac{58-2\sqrt{949}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{949}}{2*6}=\frac{58+2\sqrt{949}}{12} $
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