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(4x-3)(2x-7)+12=8
We move all terms to the left:
(4x-3)(2x-7)+12-(8)=0
We add all the numbers together, and all the variables
(4x-3)(2x-7)+4=0
We multiply parentheses ..
(+8x^2-28x-6x+21)+4=0
We get rid of parentheses
8x^2-28x-6x+21+4=0
We add all the numbers together, and all the variables
8x^2-34x+25=0
a = 8; b = -34; c = +25;
Δ = b2-4ac
Δ = -342-4·8·25
Δ = 356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{89}}{2*8}=\frac{34-2\sqrt{89}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{89}}{2*8}=\frac{34+2\sqrt{89}}{16} $
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