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(3x-4)(4x-10)=9
We move all terms to the left:
(3x-4)(4x-10)-(9)=0
We multiply parentheses ..
(+12x^2-30x-16x+40)-9=0
We get rid of parentheses
12x^2-30x-16x+40-9=0
We add all the numbers together, and all the variables
12x^2-46x+31=0
a = 12; b = -46; c = +31;
Δ = b2-4ac
Δ = -462-4·12·31
Δ = 628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{157}}{2*12}=\frac{46-2\sqrt{157}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{157}}{2*12}=\frac{46+2\sqrt{157}}{24} $
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