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6x(8x+7)-7=7(9x+8)
We move all terms to the left:
6x(8x+7)-7-(7(9x+8))=0
We multiply parentheses
48x^2+42x-(7(9x+8))-7=0
We calculate terms in parentheses: -(7(9x+8)), so:We get rid of parentheses
7(9x+8)
We multiply parentheses
63x+56
Back to the equation:
-(63x+56)
48x^2+42x-63x-56-7=0
We add all the numbers together, and all the variables
48x^2-21x-63=0
a = 48; b = -21; c = -63;
Δ = b2-4ac
Δ = -212-4·48·(-63)
Δ = 12537
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12537}=\sqrt{9*1393}=\sqrt{9}*\sqrt{1393}=3\sqrt{1393}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{1393}}{2*48}=\frac{21-3\sqrt{1393}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{1393}}{2*48}=\frac{21+3\sqrt{1393}}{96} $
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