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(6x+7)(9x-8)=7-18x*82-3x)
We move all terms to the left:
(6x+7)(9x-8)-(7-18x*82-3x))=0
We add all the numbers together, and all the variables
(6x+7)(9x-8)-(-3x-18x*82+7))=0
We get rid of parentheses
(6x+7)(9x-8)+3x+18x*82-7)=0
We multiply parentheses ..
(+54x^2-48x+63x-56)+3x+18x*82-7)=0
We add all the numbers together, and all the variables
(+54x^2-48x+63x-56)+3x+18x*82=0
Wy multiply elements
(+54x^2-48x+63x-56)+3x+1476x=0
We get rid of parentheses
54x^2-48x+63x+3x+1476x-56=0
We add all the numbers together, and all the variables
54x^2+1494x-56=0
a = 54; b = 1494; c = -56;
Δ = b2-4ac
Δ = 14942-4·54·(-56)
Δ = 2244132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2244132}=\sqrt{36*62337}=\sqrt{36}*\sqrt{62337}=6\sqrt{62337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1494)-6\sqrt{62337}}{2*54}=\frac{-1494-6\sqrt{62337}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1494)+6\sqrt{62337}}{2*54}=\frac{-1494+6\sqrt{62337}}{108} $
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