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7x-5+12x^2=-3x
We move all terms to the left:
7x-5+12x^2-(-3x)=0
We get rid of parentheses
12x^2+7x+3x-5=0
We add all the numbers together, and all the variables
12x^2+10x-5=0
a = 12; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·12·(-5)
Δ = 340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*12}=\frac{-10-2\sqrt{85}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*12}=\frac{-10+2\sqrt{85}}{24} $
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