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-6x^2-17x+14=4-7x
We move all terms to the left:
-6x^2-17x+14-(4-7x)=0
We add all the numbers together, and all the variables
-6x^2-17x-(-7x+4)+14=0
We get rid of parentheses
-6x^2-17x+7x-4+14=0
We add all the numbers together, and all the variables
-6x^2-10x+10=0
a = -6; b = -10; c = +10;
Δ = b2-4ac
Δ = -102-4·(-6)·10
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*-6}=\frac{10-2\sqrt{85}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*-6}=\frac{10+2\sqrt{85}}{-12} $
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