6x=-4x^2+7

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

6x=-4x^2+7

We move all terms to the left:

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

We get rid of parentheses

4x^2+6x-7=0

a = 4; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·4·(-7)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*4}=\frac{-6-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*4}=\frac{-6+2\sqrt{37}}{8}
$