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(3x+23)+95(7x-4)(9x-6)=540
We move all terms to the left:
(3x+23)+95(7x-4)(9x-6)-(540)=0
We get rid of parentheses
3x+95(7x-4)(9x-6)+23-540=0
We multiply parentheses ..
95(+63x^2-42x-36x+24)+3x+23-540=0
We add all the numbers together, and all the variables
95(+63x^2-42x-36x+24)+3x-517=0
We multiply parentheses
5985x^2-3990x-3420x+3x+2280-517=0
We add all the numbers together, and all the variables
5985x^2-7407x+1763=0
a = 5985; b = -7407; c = +1763;
Δ = b2-4ac
Δ = -74072-4·5985·1763
Δ = 12657429
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12657429}=\sqrt{9*1406381}=\sqrt{9}*\sqrt{1406381}=3\sqrt{1406381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7407)-3\sqrt{1406381}}{2*5985}=\frac{7407-3\sqrt{1406381}}{11970} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7407)+3\sqrt{1406381}}{2*5985}=\frac{7407+3\sqrt{1406381}}{11970} $
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