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(6x-7)(8x-9)=180
We move all terms to the left:
(6x-7)(8x-9)-(180)=0
We multiply parentheses ..
(+48x^2-54x-56x+63)-180=0
We get rid of parentheses
48x^2-54x-56x+63-180=0
We add all the numbers together, and all the variables
48x^2-110x-117=0
a = 48; b = -110; c = -117;
Δ = b2-4ac
Δ = -1102-4·48·(-117)
Δ = 34564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34564}=\sqrt{4*8641}=\sqrt{4}*\sqrt{8641}=2\sqrt{8641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{8641}}{2*48}=\frac{110-2\sqrt{8641}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{8641}}{2*48}=\frac{110+2\sqrt{8641}}{96} $
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