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(4x+2)(3x-7)=180
We move all terms to the left:
(4x+2)(3x-7)-(180)=0
We multiply parentheses ..
(+12x^2-28x+6x-14)-180=0
We get rid of parentheses
12x^2-28x+6x-14-180=0
We add all the numbers together, and all the variables
12x^2-22x-194=0
a = 12; b = -22; c = -194;
Δ = b2-4ac
Δ = -222-4·12·(-194)
Δ = 9796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9796}=\sqrt{4*2449}=\sqrt{4}*\sqrt{2449}=2\sqrt{2449}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{2449}}{2*12}=\frac{22-2\sqrt{2449}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{2449}}{2*12}=\frac{22+2\sqrt{2449}}{24} $
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