42x-35=10x-12x^2

Solution for 42x-35=10x-12x^2 equation:

42x-35=10x-12x^2

We move all terms to the left:

42x-35-(10x-12x^2)=0

We get rid of parentheses

12x^2-10x+42x-35=0

We add all the numbers together, and all the variables

12x^2+32x-35=0

a = 12; b = 32; c = -35;
Δ = b2-4ac
Δ = 322-4·12·(-35)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-52}{2*12}=\frac{-84}{24}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+52}{2*12}=\frac{20}{24}
=5/6
$