42x^2+10x-12=7x^2-3x

Solution for 42x^2+10x-12=7x^2-3x equation:

42x^2+10x-12=7x^2-3x

We move all terms to the left:

42x^2+10x-12-(7x^2-3x)=0

We get rid of parentheses

42x^2-7x^2+10x+3x-12=0

We add all the numbers together, and all the variables

35x^2+13x-12=0

a = 35; b = 13; c = -12;
Δ = b2-4ac
Δ = 132-4·35·(-12)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-43}{2*35}=\frac{-56}{70}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+43}{2*35}=\frac{30}{70}
=3/7
$