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5x^2+7=13x^2+10x
We move all terms to the left:
5x^2+7-(13x^2+10x)=0
We get rid of parentheses
5x^2-13x^2-10x+7=0
We add all the numbers together, and all the variables
-8x^2-10x+7=0
a = -8; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-8)·7
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18}{2*-8}=\frac{-8}{-16} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18}{2*-8}=\frac{28}{-16} =-1+3/4 $
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