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7x-8x^2=5x-6
We move all terms to the left:
7x-8x^2-(5x-6)=0
We get rid of parentheses
-8x^2+7x-5x+6=0
We add all the numbers together, and all the variables
-8x^2+2x+6=0
a = -8; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-8)·6
Δ = 196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-8}=\frac{-16}{-16} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-8}=\frac{12}{-16} =-3/4 $
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