7x^2+5x+4=6x^2+2x+39

Solution for 7x^2+5x+4=6x^2+2x+39 equation:

7x^2+5x+4=6x^2+2x+39

We move all terms to the left:

7x^2+5x+4-(6x^2+2x+39)=0

We get rid of parentheses

7x^2-6x^2+5x-2x-39+4=0

We add all the numbers together, and all the variables

x^2+3x-35=0

a = 1; b = 3; c = -35;
Δ = b2-4ac
Δ = 32-4·1·(-35)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{149}}{2*1}=\frac{-3-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*1}=\frac{-3+\sqrt{149}}{2}
$